Question

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)

Answer 1

@jim_thompson5910

Answer 2

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

Answer 3

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

Answer 4

is that right so far??

Answer 5

notice how 2 is a factor in each, so we can factor out 2

8x^2+22x-6 = 2(4x^2+11x - 3)

Answer 6

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

Answer 7

Wouldn't you start simplifying the problem?

Answer 8

multiply the first coefficient (4) and the last term (-3)

4*(-3) = -12

what two factors of -12 add to 11 ?

Answer 9

put another way:

what two numbers multiply to -12 and add to 11?

Answer 10

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

Answer 11

I'm not combining like terms

Answer 12

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

Answer 13

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

Answer 14

-12 could be 6,2,3,4

Answer 15

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?

Answer 16

The first one

Answer 17

yep

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

Answer 18

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

Answer 19

Oh okay...

Answer 20

4x^2+11x - 3

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

Answer 21

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

Answer 22

group up the terms in pairs

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

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

do you see what step is next?

Answer 23

Simplify them.

Answer 24

specifically you factor each group

Answer 25

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

Answer 26

I don't know?

Answer 27

we can factor out x, agreed?

4x^2 - 1x = x(4x - 1)

Answer 28

oh yeah since they are like terms

Answer 29

how would you factor 12x - 3 ?

Answer 30

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

Answer 31

what factors do 12 and 3 have in common?

Answer 32

12x and -3 aren't like terms

Answer 33

oh duh 3

Answer 34

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

Answer 35

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

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

x(4x - 1) + 3(4x - 1)

Answer 36

what factor shows up twice?

Answer 37

one

Answer 38

what else

Answer 39

4

Answer 40

the 4x-1 shows up twice

Answer 41

we can factor that out

x(4x - 1) + 3(4x - 1)

will turn into

(x+3)(4x - 1)

Answer 42

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

Answer 43

I think so

Answer 44

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

Answer 45

Okay