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

- anonymous

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

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- mathteacher1729

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

- anonymous

4

- anonymous

right?

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## More answers

- mathteacher1729

Yup. So now write
4 times (whatever is left over after you factor out 4)

- anonymous

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

- mathteacher1729

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).

- anonymous

well that is where i'm confused

- anonymous

how do i know what number to choose?

- mathteacher1729

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

- anonymous

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

- anonymous

is there anything i can do?

- mathteacher1729

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. :)

- anonymous

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

- mathteacher1729

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

- anonymous

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

- mathteacher1729

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.

- anonymous

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

- mathteacher1729

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...

- anonymous

okay
is it 4 and 8

- mathteacher1729

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

- anonymous

(7b-4)(b+8)

- mathteacher1729

Let's factor that out now:
(7b-4)(b+8)
7b^2 (good)
-4b +56b = 52b (nope)
8 * -4 = -32 (good)

- mathteacher1729

You are VERY close though!

- anonymous

i don't know where to go from there

- anonymous

i'm stuck

- anonymous

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

- mathteacher1729

No, because -1 * 2 = -2.
You were right, it's 4 and 8.
But the order and the sign need to be tweaked.

- anonymous

what do u mean?

- mathteacher1729

(7b )(b )
Fill in the blanks with 4 and 8. One of the combinations will work. :)

- mathteacher1729

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.

- mathteacher1729

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. :)

- anonymous

okay thank you!

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