Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Example 3: Factor a quartic binomial with two variables by taking a common factor | Khan Academy

Video vocabulary

fourth

Copy vocabulary

US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

both

Copy vocabulary

US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

way

Copy vocabulary

US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

common

Copy vocabulary

US / 'kɒmən /

UK / ˈkɑmən /

A1
  • adjecitve
  • Shared; Belonging to or used by everyone
  • Typical, normal; not unusual
  • noun
  • Area in a city or town that is open to everyone
  • Field near a village owned by the local community

possible

Copy vocabulary

US / ˈpɒsəbl /

UK / ˈpɑsəbəl /

A1
  • adjecitve
  • Being able or appropriate for a task or purpose
  • Having a chance of happening, or being true

pretty

Copy vocabulary

US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

general

Copy vocabulary

US / 'dʒenrəl /

UK / ˈdʒɛnərəl /

A1
  • adjecitve
  • Widespread, normal or usual
  • noun
  • Top ranked officer in the army

everything

Copy vocabulary

US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

look

Copy vocabulary

US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

its

Copy vocabulary

US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

fast

Copy vocabulary

US / fɑ:st /

UK / fæst /

A1
  • adjecitve
  • In a way that is difficult to move or change
  • Moving or able to move quickly
  • Showing time that is later than the actual time
  • adverb
  • With a great deal of speed
  • noun
  • Period of time when a person chooses not to eat
  • verb
  • To refuse food for a long time

monomial

Copy vocabulary

US / /

UK / /

A1
  • other

expression

Copy vocabulary

US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

rewrite

Copy vocabulary

US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

cancel

Copy vocabulary

US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

multiply

Copy vocabulary

US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

basic

Copy vocabulary

US / 'beɪsɪk /

UK / ˈbesɪk /

A1
  • adjecitve
  • At the most important or easiest (beginner) level

code

Copy vocabulary

US / kəʊd /

UK / kod /

A2
  • noun
  • A password made of a set of letters or numbers
  • Set of rules for behavior
  • A secret language using secret symbols
  • Written part of a computer program
  • verb
  • To express information in a series of numbers
  • To write a secret message using secret symbols
  • To write programs using computer languages

contain

Copy vocabulary

US / kənˈteɪn /

UK / kənˈten /

A2
  • verb
  • To keep something from spreading
  • To hold something inside something else

itself

Copy vocabulary

US / ɪtˈself /

UK / ɪtˈsɛlf /

A1
  • pronoun
  • Referring to it

always

Copy vocabulary

US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

should

Copy vocabulary

US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

speak

Copy vocabulary

US / spi:k /

UK / spik /

A1
  • verb
  • To be able to use a certain language
  • To use words to tell information, express thoughts

many

Copy vocabulary

US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

exactly

Copy vocabulary

US / ɪgˈzæktli /

UK / ɪɡˈzæktli /

A1
  • adverb
  • No more and no less than; precisely

third

Copy vocabulary

US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

divide

Copy vocabulary

US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

four

Copy vocabulary

US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

negative

Copy vocabulary

US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

prime

Copy vocabulary

US / praɪm /

UK / praɪm /

A2
  • adjecitve
  • Concerning the highest in quality or value
  • Concerning the highest level of achievement
  • Most important, chief importance in value
  • verb
  • To get a person ready for; prepare someone
  • To coat with paint to prepare it for the main coat

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

clear

Copy vocabulary

US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

process

Copy vocabulary

US / prə'ses /

UK / ˈprɑsˌɛs, ˈproˌsɛs /

A2
  • noun
  • Dealing with official forms in the way required
  • Set of changes that occur slowly and naturally
  • verb
  • To organize and use data in a computer
  • To deal with official forms in the way required
  • To prepare by treating something in a certain way
  • To adopt a set of actions that produce a result
  • To convert by putting something through a machine

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

most

Copy vocabulary

US / məʊst /

UK / most /

A1
  • adverb
  • Very; extremely
  • Greatest possible degree
  • pronoun
  • Nearly all of something

leave

Copy vocabulary

US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

large

Copy vocabulary

US / lɑ:dʒ /

UK / lɑ:rdʒ /

A1
  • adjecitve
  • Big; of great size; broad, tall, wide, or fat

two

Copy vocabulary

US / tu: /

UK / tu /

A1
  • number
  • 2

hopefully

Copy vocabulary

US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

only

Copy vocabulary

US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

put

Copy vocabulary

US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

another

Copy vocabulary

US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

where

Copy vocabulary

US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

tell

Copy vocabulary

US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

like

Copy vocabulary

US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

absolute

Copy vocabulary

US / ˈæbsəlu:t /

UK / ˈæbsəˌlut /

A2
  • adjecitve
  • Complete; total; pure; not limited in any way
  • noun
  • Something that is complete, total, pure, certain

include

Copy vocabulary

US / ɪnˈklu:d /

UK / ɪnˈklud /

A1
  • verb
  • To make someone, something part of a group

mean

Copy vocabulary

US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

essentially

Copy vocabulary

US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

find

Copy vocabulary

US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

expand

Copy vocabulary

US / ɪk'spænd /

UK / ɪkˈspænd /

A2
  • verb
  • To make something larger in size, number, amount

number

Copy vocabulary

US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

each

Copy vocabulary

US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

eventually

Copy vocabulary

US / ɪˈventʃuəli /

UK / ɪˈvɛntʃuəli /

A2
  • adverb
  • After a long time; after many attempts; in the end

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

similar

Copy vocabulary

US / ˈsɪmələ(r) /

UK / ˈsɪməlɚ /

A1
  • adjecitve
  • Nearly the same; alike

great

Copy vocabulary

US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

multiple

Copy vocabulary

US / ˈmʌltɪpl /

UK / ˈmʌltəpəl /

B1
  • adjecitve
  • Having or involving more than one of something
  • noun
  • Number produced by multiplying a smaller number
  • Shop with many branches

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

term

Copy vocabulary

US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

less

Copy vocabulary

US / les /

UK / lɛs /

A1
  • adjecitve
  • Smaller in amount or degree
  • adverb
  • To a smaller degree
  • noun
  • A smaller amount
  • preposition
  • With the subtraction of

quote

Copy vocabulary

US / kwəʊt /

UK / kwot /

A2
  • noun
  • Written statement of the cost of something
  • The (often wise or famous) words of another person
  • verb
  • To tell someone how much a task will cost
  • To repeat precisely what a person said or wrote

three

Copy vocabulary

US / θri: /

UK / θri /

A1
  • number
  • Number 3

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

other

Copy vocabulary

US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

into

Copy vocabulary

US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

kind

Copy vocabulary

US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

than

Copy vocabulary

US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

would

Copy vocabulary

US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

distribute

Copy vocabulary

US / dɪˈstrɪbju:t /

UK / dɪˈstrɪbjut /

A2
  • verb
  • To hand out or give to people
  • To send products to stores to sell
  • To spread something over an area

give

Copy vocabulary

US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

become

Copy vocabulary

US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

sense

Copy vocabulary

US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

quotes

Copy vocabulary

US / kwəʊts /

UK / kwoʊts /

B1
  • other
  • Written statement of the cost of something
  • The (often wise or famous) words of people
  • verb
  • To tell someone how much a task will cost
  • To repeat precisely what a person said or wrote

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

expansion

Copy vocabulary

US / ɪkˈspænʃn /

UK / ɪkˈspænʃən /

B2
  • noun
  • Making or becoming larger

color

Copy vocabulary

US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

factorization

Copy vocabulary

US / ˌfæktəraɪˈzeɪʃən /

UK / ˌfæktərəˈzeɪʃən /

A1
  • noun
  • Resolution of an entity into factors such that when multiplied together they give the original entit

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

really

Copy vocabulary

US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

whether

Copy vocabulary

US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

head

Copy vocabulary

US / hed /

UK / hɛd /

A1
  • noun
  • Counter for the number of cattle
  • Natural mental ability or intelligence
  • Leader or person with the greatest authority
  • Mind; mental ability; mental state
  • Side of a coin with a head on it
  • Top part of your body with eyes and a mouth
  • Starting point of something, e.g. a river
  • verb
  • To hit a ball with your head in a game
  • To be first or at the front or top (e.g. a list)
  • To travel or move toward a particular place; To go in a particular direction
  • To become the leader of something
  • To lead or be responsible for something

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

algebraic

Copy vocabulary

US / ˌældʒɪ'breɪɪk /

UK / ˌældʒəˈbreɪk /

C1
  • adjecitve
  • Concerning algebra

situation

Copy vocabulary

US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

positive

Copy vocabulary

US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

stuff

Copy vocabulary

US / stʌf /

UK / stʌf /

A1
  • noun
  • Generic description for things, materials, objects
  • verb
  • To push material inside something, with force

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

exact

Copy vocabulary

US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

through

Copy vocabulary

US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

constituent

Copy vocabulary

US / kənˈstɪtjuənt /

UK / kənˈstɪtʃuənt /

C2
  • noun
  • Necessary part or element of something else

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

numerator

Copy vocabulary

US / ˈnju:məreɪtə(r) /

UK / ˈnu:məreɪtə(r) /

C2
  • noun
  • Dividend of a fraction

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)
  • Subtitles section
  • Factor out the greatest common factor.
  • And the expression they give us is 4x to the fourth y plus 8x to the third y.
  • When they say to factor out the greatest common factor they're essentially telling us, find the greatest common factor of 4x to the fourth and 8x to the third y and factor it out of this expression.
  • Or kind of undistribute it.
  • And to find that greatest common factor-- and I always put it in quotes when we speak in algebraic terms.
  • Because we don't really know what x and y are, whether they're positive or negative or whether they're greater than or less than 1.
  • So it's not always going to be the greatest absolute number.
  • But it's the greatest in it contains the most terms of these two expressions, these two monomials.
  • So if we were to essentially factor out 4x to the fourth y it would look like this.
  • We would do the prime factorization of 4, which is just 2 times 2, times x to the fourth, which is x times x times x times x, times y.
  • We just expanded it out as a product of its basic constituents.
  • Now let's do the same thing for 8-- I'll color code it-- 8x to the third.
  • Let me do it in similar colors.
  • So in this situation we have 8x to the 1/3 y.
  • So the prime factorization of 8 is 2 times 2 times 2.
  • It's 2 times 2 times 2.
  • Prime, or I should say the factorization of x to the third, or the expansion of it, is just times x times x times x. x multiplied by itself three times.
  • And then we are multiplying everything by a y here, times y.
  • So what factors are common to both of these?
  • And we want to include as many of them as possible to find this greatest common factor.
  • So we have two 2's here, three 2's here.
  • So we only have two 2's in common in both of them.
  • We have four x's here, only three x's here.
  • So we only have three x's in common.
  • Three x's and three x's.
  • And we have a y here and a y here.
  • So y is common to both expressions.
  • So the greatest common factor here is going to be 2 times 2.
  • So it's going to be 2 times 2 times x times x times x times y.
  • Or 4x to the third y.
  • So this is what we want to factor out.
  • So that means we can write this thing as-- if we factor out a 4x to the third y, where essentially we have to divide each of these by 4x to the third.
  • We're factoring it out.
  • So let me rewrite this.
  • So this is 4x to the fourth y plus 8x to the third y.
  • And we're going to divide each of these by 4x to the third y.
  • And hopefully this makes sense to you.
  • If we were to multiply this out, we would distribute this 4x to the third y on each terms.
  • And then it would cancel with the denominator.
  • You would have the same thing in the numerator and denominator.
  • And then you would get this expression over here.
  • So hopefully this makes sense that these are the exact same expression.
  • But when you write it this way, then it becomes pretty clear that this is 4x to the third y.
  • And then you just simplify each of these expressions.
  • 4 cancels with 4. x to the fourth divided by x to the third is x.
  • y divided by y is just 1.
  • So you have x plus 8 divided by 4 is 2.
  • x to the third divided by x to the third is 1.
  • Y divided by y is 1.
  • So x plus 2.
  • Another way to see what's left over when you factor it out is if you were to take out the common factor.
  • So we took out this and this.
  • What was left over in 4x to the fourth y when we took this stuff out?
  • When we undistributed it?
  • Well, the only thing that was left was this x right over here.
  • Let me do that in another color.
  • The only thing that was left was this x.
  • So that's why we just have that x over there.
  • When we factored everything out of the 8x to the third y we factored all this other stuff out.
  • We factored out 4x to the third y.
  • We factored it out, so all we had left was the 2.
  • Now in general, you don't always have to go through this process.
  • You could have done it this way, but this really hopefully makes it clear exactly what we're doing.
  • You could have said, look, 4x to the fourth y plus 8x to the third y.
  • You could have said, well let's see, the largest number that's divisible into both 4 an 8 is 4.
  • So let's factor out a 4 out here.
  • The largest multiple of x that's divisible into x to the fourth and x to the third, well that's going to be x to the third.
  • And you put an x to the third out here.
  • And you say, well, the largest thing that's divisible both into y and y is just y.
  • So you could have done it a little bit faster in your head.
  • So you factor out a 4x to the third and you say, OK, if I take out a 4 out of here, then this becomes a 1.
  • If I take an x to the third out of x to the fourth I'll just have an x left over.
  • And then if I take a y out of the y then I just have a 1 there.
  • So this term becomes x.
  • And then if I take a 4x to the third y out of here, if I take a 4 out of an 8 I just have a 2 left over.
  • If I take an x to the third out of x to the third, that's just 1.
  • If I take y out of y, that's just one.
  • So I'm just left with x plus 2.
  • Eventually you'll just do this in your head a little bit faster.
  • But hopefully this makes everything clear.