factor
## Learn the ac method for factoring and solving a quadratic equation

again ladies and gentlemen when we're

looking at this when we're looking at a

problem like this basically again what

we want to be able to do is same exact

thing you know I'm not going to do a box

but the same idea is going to apply we

still need to figure out we want to be

able to rewrite our middle term as two

separate values and rather than filling

them in a box we're going to factor by

grouping which we actually talked about

before in this class but either way the

first thing we need to do is do a times

C a times C 9 times 5 negative 5 is

negative 45 and then to add to give us

negative 12

now I get a lot of students that get

stuck in the same miss from going I

don't know you know what to do you know

next the most important thing that I

would say guys even if you get stuck all

right even if you can't figure it out on

your test write down all of the factors

of 45 all right and this isn't that

difficult the way that I want you to do

it is always the obviously you can

always start with 45 times one then just

start working with numbers go from one

now let's say 2 is 2 divisible into 45

no it's not right so then we go to 3 is

3 divisible into 45 yes

so you could say 3 times 15 then work

your way up

what about 4 is 4 divisible in the 45 no

go to 5 it's 5 divisible in the 45 yes

and then we go up to 6 is 6 divisible

into 45 no 7 no hope 8 nope and then I

get back up to 9 which I already know is

divisible so therefore I'm all done so

these are the only factors now we are

multiplying to give us negative 45 so

just think listen to my mind my thought

process it has to multiply to give you

negative 45 and add to give you negative

if you're adding a positive and a

negative number and your answer is

negative should sort the negative or the

positive number be larger in absolute

value the negative number should be

larger

think about it negative five plus three

an absolute value which one is larger

the five or the three the five right so

a larger negative five absolute value of

it plus three is going to equal negative

two right it's going to give you a

negative number so therefore since I'm

adding these two Vout since I'm adding

these two factors and my the sum is

negative then my larger factor has to be

negative and now when I look at this

Ashley which of these add up to give me

negative 12 negative 15 and positive 3

now I'm gonna do just like what I did

last time but I'm not gonna fill it into

a box I'm gonna say 9x squared and then

I'm gonna say minus 15 X plus 3x minus 5

equals 0 does everybody see what I did I

just rewrote the I just rewrote the

equation that's all I did I didn't

change it or do anything else with it I

didn't put it in a box I just rewrote it

just but I mean I showed you guys how to

rewrite this last time and now what we

can do is a prize like factoring

techniques which we call grouping where

you group the first two terms and you

group the last two terms and basically

what we have already done in this class

is we talked about grouping but we also

talked about factoring out the GCF now

all you're simply going to do is factor

the GCF out of each of these expressions

so we look at the first two and say what

do these have in common what is their my

common factor you could say a 3x and

when you factor out a 3x you're left

with 3x minus 5 then I look over here

and I say is there anything I can factor

out of these no so therefore I can

factor out a positive 1 you're always

going to have to factor out something

and if they don't have anything in

common then factor out a positive or a

negative one okay Tyler and then what

therefore we're left with 3x minus 5

now what you guys can see is that the 3x

minus 5 is common between both of these

terms or both of these expressions right

do you guys see I have two expressions

that are separated by addition and

therefore now you factor those out you

factor out what they have in common

which is I don't want to write this like

that so therefore that's 3x minus 5

times 3x plus 1 equals 0 now you can

apply the zero-product property and

therefore I'm not going to show you the

steps to solving and get them all done

now you could do that exact same one by

using the

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