# How to Factor Polynomial

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In this video tutorial, I talked about how to factor polynomial using AC method.

Video by shawnkoon

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what’s up guys it’s me Shawn here with

some math tutorial here today and today

we’re going to learn how to factor a

polynomial so let’s get started so the

first thing you have to do is you have

to choose a question so what I did was I

chose this 12x squared plus 5x minus 2

as my practice problem so before we go

into solving what are they mean by

factor factor is pretty much saying you

want to convert this polynomial into the

form that looks something like this

so parenthesis term times parenthesis

term so that’s what’s called factoring

so we’re trying to convert this

polynomial into that factored form so

how do we do that I use this thing

called a AC method and this pretty much

works like charm on every kind of

polynomials if you want to factor and

stuff and if it if this way doesn’t work

out that pretty much means it’s a prime

okay

so let’s get started so before we get

into AC method here we have to know that

in front of what’s x squared it’s called

a so the coefficient in front of x

squared is a and coefficient in front of

X is called B and the last one the

constant is called C and if you have

learned quadratic formula you have to

know how to figure these out right so we

have that a is equal to 12 and B is

equal to 5

and C is equal to negative two right so

let’s use AC method so AC method the

reason we call AC is because we multiply

a and C so let’s do that what’s 12 times

negative 2 yes that’s negative 24 right

so what what we were trying to do here

is we have to find a two numbers that

multiply together to get negative 12 24

but when you combine those two you get a

plus 5 okay so there’s two things we

have to watch out for so let’s start

with number one so 1 times 24 one of

them has to be negative but let’s say I

do this one negative can I get five if I

combine these two No so this one’s not

it how about 2 and 12 if I put negative

here I might get closer to 5 but not if

not quite yet so what we have to do is

we have to move on to next one how about

3 & 8 whoo that seems like it’s going to

work so one of them has to be negative

right so negative 3 plus 8 becomes 5 so

this works out so I know that my AC

method solution is these 2 so now what

we got to do here is we have to break

this middle term here into two different

sections so we have 12

x-square just bring it down okay

and what you’re going to do is you’re

going to take this five and break it

into these two the one we just found so

negative 3x + + 8 X + – 2 because we’re

going to bring this down just like that

okay so now we have four terms here our

next step is to group them so by mean is

we’re going to group two terms like that

all righty

and the third step here is we have to

factor out the common numbers from each

of these terms so out of these two

notice I can pull out an X right because

X is in common but also I can pull out

on 3 because 3 goes into 12 so I’m going

to factor out 3 and X at the same time

so I get 4x left over – one like that

and from here I can factor out a 2 so

I’m going to put factor out + 2 and I’m

left over with 4x – 1 nice so how do we

know if we can make any mistakes we can

tell by looking at these two terms if

these two terms matches up that means we

are good

okay so now the last step here is we

have to combine these two into one and

we have to combine these two into one so

3x + 2 becomes our 1 term and 4x plus a

minus 1 becomes our second term and that

is our answer so yeah that’s how you use

AC method to solve a factoring problem

you

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