Which of the following is polynomial factor of 8x^2+22x-6?
A (4x-3)
B (4x+3)
C (8x-2)
D (8x+3)
E (8x+6)

- tootsi123

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- tootsi123

@jim_thompson5910

- jim_thompson5910

what is the GCF of 8,22, and 6 ?

- tootsi123

Oh wait i think i get it hold on...
8= 2^3
22=2*11
6=2*3

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## More answers

- tootsi123

is that right so far??

- jim_thompson5910

notice how 2 is a factor in each, so we can factor out 2
8x^2+22x-6 = 2(4x^2+11x - 3)

- jim_thompson5910

how would we factor 4x^2+11x - 3 ?

- tootsi123

Wouldn't you start simplifying the problem?

- jim_thompson5910

multiply the first coefficient (4) and the last term (-3)
4*(-3) = -12
what two factors of -12 add to 11 ?

- jim_thompson5910

put another way:
what two numbers multiply to -12 and add to 11?

- tootsi123

Wait i am confused... i thought you couldn't combine terms unless they were like terms.... and would 3 be one

- jim_thompson5910

I'm not combining like terms

- jim_thompson5910

I'm asking for the two numbers because it will help factor

- tootsi123

oh. Okay so 11 is a prime number so its only factor is one.

- tootsi123

-12 could be 6,2,3,4

- jim_thompson5910

here are all of the ways to multiply two whole numbers to get -12
-1*12
-2*6
-3*4
-4*3
-6*2
-12*1
which pair of factors will add up to 11?

- tootsi123

The first one

- jim_thompson5910

yep
-1*12 = -12
-1 + 12 = 11

- jim_thompson5910

so we can break up the 11x into -1x + 12x

- tootsi123

Oh okay...

- jim_thompson5910

4x^2+11x - 3
4x^2-1x + 12x - 3

- jim_thompson5910

then we'd factor 4x^2-1x + 12x - 3 by grouping

- jim_thompson5910

group up the terms in pairs
4x^2-1x + 12x - 3
(4x^2-1x) + (12x - 3)
do you see what step is next?

- tootsi123

Simplify them.

- jim_thompson5910

specifically you factor each group

- jim_thompson5910

how can you factor 4x^2-1x ?

- tootsi123

I don't know?

- jim_thompson5910

we can factor out x, agreed?
4x^2 - 1x = x(4x - 1)

- tootsi123

oh yeah since they are like terms

- jim_thompson5910

how would you factor 12x - 3 ?

- tootsi123

Wouldn't you just do 12 -3 and then add the x

- jim_thompson5910

what factors do 12 and 3 have in common?

- jim_thompson5910

12x and -3 aren't like terms

- tootsi123

oh duh 3

- jim_thompson5910

yeah so 12x - 3 = 3(4x - 1)

- jim_thompson5910

4x^2-1x + 12x - 3
(4x^2-1x) + (12x - 3)
x(4x - 1) + 3(4x - 1)

- jim_thompson5910

what factor shows up twice?

- tootsi123

one

- jim_thompson5910

what else

- tootsi123

4

- jim_thompson5910

the 4x-1 shows up twice

- jim_thompson5910

we can factor that out
x(4x - 1) + 3(4x - 1)
will turn into
(x+3)(4x - 1)

- jim_thompson5910

so hopefully you see how 8x^2+22x-6 factors to 2(x+3)(4x - 1)

- tootsi123

I think so

- jim_thompson5910

go over the steps a few times to make sure you have a solid grasp of it. you can ask questions if you aren't sure about a step or two

- tootsi123

Okay

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