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U09_L1_T2_we3 Factoring Trinomials by Grouping 3

Video vocabulary

all

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US / ɔ:l /

UK / ɔl /

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

common

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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

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

way

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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

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

close

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US / kləʊz /

UK / kloʊz /

A1
  • adjecitve
  • Almost; near
  • (Of a friend) well-known; liked by others
  • Being near or related
  • Similar; nearly the same
  • verb
  • To come progressively nearer to something
  • To end; to bring to an end
  • To make something shut; stop from being open

take

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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

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

swap

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US / swɒp /

UK / swɑp /

B2
  • noun
  • A trade or exchange of goods without using money
  • verb
  • To exchange goods without spending money; trade

they

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US / ðeɪ /

UK / ðe /

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

both

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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

simple

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US / 'sɪmpl /

UK / ˈsɪmpəl /

A1
  • adjecitve
  • Not hard to understand or do; not complex
  • Having only a few parts; not complex
  • Being ordinary or normal
  • Being plain; without a lot added for style

look

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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

plus

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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

ever

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US / 'evə(r) /

UK / ˈɛvɚ /

A1
  • adverb
  • At any time; at all times in the future

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

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

here

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US / hɪə(r) /

UK / hɪr /

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

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

can

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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

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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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

but

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US / bət /

UK / bʌt,bət /

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

not

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US / nɒt /

UK / nɑt /

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

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

sum

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US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

want

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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

combination

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US / ˌkɒmbɪ'neɪʃn /

UK / ˌkɑmbəˈneʃən /

B1
  • noun
  • Series of letters or numbers needed to open a lock
  • Act or result of mixing things together

positive

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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

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

well

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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

time

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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

just

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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)

anywhere

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US / ˈeniweə(r) /

UK / ˈeniwer /

A1
  • adverb
  • To any extent or degree (often used with not)
  • In, at or to any place
  • other
  • Use to indicate limits or variation

and

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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

front

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US / frʌnt /

UK / frʌnt /

A1
  • adjecitve
  • Opposite of back; the forward part of an object
  • noun
  • Behavior not showing a person's true feelings
  • Area where fighting in a war is happening
  • Place where air of different temperatures meets
  • verb
  • To have the forward part facing something
  • To lead a group of people, usually a band

put

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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

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

out

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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

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

leave

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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

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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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

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon
  • verb
  • To agree to support a proposal at a meeting

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

then

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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

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

that

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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’

what

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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

right

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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

interesting

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US / ˈɪntrəstɪŋ /

UK / ˈɪntrɪstɪŋ, -tərɪstɪŋ, -təˌrɛstɪŋ /

A1
  • adjecitve
  • Taking your attention; making you want to know
  • verb
  • To make someone want to know about something
  • To persuade to do, become involved with something

number

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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

tell

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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

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

find

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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

break

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US / breɪk /

UK / brek /

A1
  • noun
  • Time you stop an activity before continuing
  • End of a relationship
  • An escape from a place such as a jail
  • (Lucky) advantage or benefit from something
  • Find a solution or answer to a problem or crime
  • Change in the weather
  • verb
  • To create a new record e.g. running the 100m dash
  • To form a crack in something
  • To burst or become damaged
  • To end a relationship
  • To escape from a place such as a jail
  • To train a wild animal e.g. a horse
  • To separate into pieces by force, or by dropping
  • To act against a law, rule, or promise
  • To become known suddenly, as in the news
  • To not do what you promised e.g. not keep promises
  • To solve a crime, or answer a problem
  • To stop functioning properly
  • To suddenly start, open or commence
  • To change in pitch suddenly, as in a voice
  • To fall on the shore, as in waves
  • To begin or change suddenly; the dawn or weather
  • To defeat by causing the person to lose their will

with

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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

have

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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

could

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US / kəd /

UK / kʊd /

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

negative

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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

see

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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)

group

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US / ɡru:p /

UK / ɡrup /

A1
  • noun
  • Two or more musicians who play music together
  • Number of people or things gathered together
  • verb
  • To combine or collect objects or people together

lead

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US / li:d /

UK / lid /

A1
  • adjecitve
  • Being the main part in movies or plays
  • noun
  • Wire for electricity, computer, etc.; cable
  • Information that could help to solve a crime
  • Main part in a play or movie
  • Heavy, gray metal element
  • Rope used to tie something to stop it escaping
  • Act of being at the front in a race or game
  • verb
  • To show the way or guide others
  • To be at the front of a race or game
  • To travel in front of; go in advance of others

let

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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

the

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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

you

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US / jʊ /

UK / ju /

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

ready

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US / 'redɪ /

UK / ˈrɛdi /

A1
  • adjecitve
  • Being likely or about to do something
  • Being willing to do a task
  • verb
  • To prepare something for use or action

this

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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

coefficient

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US / ˌkəʊɪˈfɪʃnt /

UK / ˌkoʊɪˈfɪʃnt /

B2
  • adjecitve
  • Number by which another number is multiplied

into

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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

than

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US / ðən /

UK / ðən /

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

whose

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US / hu:z /

UK / huz /

A1
  • pronoun
  • Refers to the person who owns something

term

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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
  • Subtitles section
  • We're told to factor r squared plus 4r, minus 45.
  • And there are simpler ways to factor this, because this has 1 as a leading coefficient on the r squared right here, but what we're going to do is we're going to factor this by grouping.
  • And when you factor it by grouping, what you want to do is find two numbers whose product-- so the two numbers are a and b-- whose product is equal to the coefficient on r squared, 1 times negative 45, which is just negative 45.
  • And whose sum is equal to the coefficient on the first degree term, is equal to 4.
  • a plus b is equal to 4.
  • So let's look at all of the different combinations that goes to negative 45, and see if when you add them, you ever get to 4.
  • So let's take the combinations.
  • Let's look at their different a's and b's, and let's see what happens when you sum them.
  • So I could try 1 and negative 45, but if you take their sum, that's not going to get you anywhere close to 4, even if you swapped them, negative 1 and positive 45.
  • Let's see, if you do 3 and 15, 3 and negative 15, or negative 3 and 15, those are way more than 4 apart.
  • We're going to have to find numbers that are closer together.
  • So let's see, 3, 4, 5 and 9, that looks interesting.
  • 5 and 9 are 4 apart.
  • And if we go with 5 and negative 9, what's their sum?
  • Their sum is negative 4.
  • What happens if we go with negative 5 and positive 9?
  • Well, then their sum is 4, so negative 5 and positive 9 works.
  • So what we want to do here, now that we found the numbers whose product is equal to the 1 times negative 45, and whose sum is equal to 4, let's break this 4r up into a sum of negative 5-- let me break it up this way-- into 9r minus 5r.
  • I broke that 4r into that using our two numbers, and then I could put the r squared out front, r squared, and then we have a minus 45.
  • And now we're ready to group this and then factor by grouping.
  • So let's look at this first group right here.
  • They both have the common factor of r, so let's factor out an r.
  • This is equal to r times-- r square divided by r is r.
  • 9r divided by r is 9.
  • So that's that first group.
  • And the second group right here, has a common factor of negative 5.
  • So let's factor it out.
  • Negative 5r divided by negative 5 is just an r.
  • Negative 45 divided by negative 5 is a 9.
  • And then we have an r plus 9 in both terms. r times r plus 9, negative 5 times r plus 9.
  • So we can factor that out.
  • So you factor an r plus 9 out, and you're left with r times r plus 9, divided by r plus 9 is just going to be an r.
  • And then negative 5 times r plus 9, divided by r plus 9 is negative 5, and we're done!