Question

how can i factor this out?
28b^2-80b-128

Answer 1

First ask yourself if there is a constant you can factor out of all the coefficients. :)

Answer 2

4

Answer 3

right?

Answer 4

Yup. So now write

4 times (whatever is left over after you factor out 4)

Answer 5

4(7b^2-20b-32) but then what do i do?

Answer 6

Now we want to factor out 7b^2-20b-32 into the product of two binomaisl:

(b plus or minus stuff) times ( b plus or minus stuff).

BUT LOOK! The coefficient of b^2 is 7, so that means we automatically know that it's going to look like...

(7b plus or minus stuff) times (b plus or minus stuff).

Answer 7

well that is where i'm confused

Answer 8

how do i know what number to choose?

Answer 9

Can you factor something like: x^2 + 10x +21 ?
It's similar to that, but just a little harder.

Answer 10

but if i factor out -32 there is nothing that would match -20

Answer 11

is there anything i can do?

Answer 12

The answer to this problem is the same as factoring something like

x^2 + 10x +21

Describe how you would factor this and then the solution to your problem will make much more sense. :)

Answer 13

is it (x+7)(x+3) ?

Answer 14

Yes! :) How did you obtain that answer? How did you know to go for +7 and +3?
Also, can you factor:

x^2 -4x -21

Answer 15

well because the numbers are positive
But i'm confused w/ my original problem

Answer 16

7b^2-20b-32 = (7b ) * ( b )

The two numbers you fill in will have to multiply to negative 32. That's the start of it.

Answer 17

right but there is 1*32,2*16,4*8

Answer 18

You have to try those out. :) ALSO note how one of those numbers is gonna be multplied by 7 when you FOIL. So it's trial and error. After a bit of practice you develop a number sense about these things.

So for instance 1 * 32 won't work...

(7b +32)(b -1)
FOIL that out and you get 7b^2
32b -7b = -25b
-31

So try the next one...

Answer 19

okay
is it 4 and 8

Answer 20

In what order? And with what signs (which is + and which is - ) ?

Answer 21

(7b-4)(b+8)

Answer 22

Let's factor that out now:

(7b-4)(b+8)

7b^2 (good)
-4b +56b = 52b (nope)
8 * -4 = -32 (good)

Answer 23

You are VERY close though!

Answer 24

i don't know where to go from there

Answer 25

i'm stuck

Answer 26

is it (7b-1)(b+2) ?

Answer 27

No, because -1 * 2 = -2.
You were right, it's 4 and 8.

But the order and the sign need to be tweaked.

Answer 28

what do u mean?

Answer 29

(7b )(b )

Fill in the blanks with 4 and 8. One of the combinations will work. :)

Answer 30

Do you know how to FOIL? (or expand) a binomial? That is the other half of solving problems like these.

Going from (7b +4)(b +8) to 7b^2 +12b +32 is critical to the trial-and-error portion.

Answer 31

Paul's Online Math Notes has a very nice explanation of this with TONS of examples: http://tutorial.math.lamar.edu/Classes/Alg/Factoring.aspx

I have to sign off, but hopefully this will help a little. :)

Answer 32

okay thank you!