anonymous
  • anonymous
how can i factor this out? 28b^2-80b-128
Mathematics
chestercat
  • chestercat
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mathteacher1729
  • mathteacher1729
First ask yourself if there is a constant you can factor out of all the coefficients. :)
anonymous
  • anonymous
4
anonymous
  • anonymous
right?

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mathteacher1729
  • mathteacher1729
Yup. So now write 4 times (whatever is left over after you factor out 4)
anonymous
  • anonymous
4(7b^2-20b-32) but then what do i do?
mathteacher1729
  • 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
  • anonymous
well that is where i'm confused
anonymous
  • anonymous
how do i know what number to choose?
mathteacher1729
  • mathteacher1729
Can you factor something like: x^2 + 10x +21 ? It's similar to that, but just a little harder.
anonymous
  • anonymous
but if i factor out -32 there is nothing that would match -20
anonymous
  • anonymous
is there anything i can do?
mathteacher1729
  • 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
  • anonymous
is it (x+7)(x+3) ?
mathteacher1729
  • 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
  • anonymous
well because the numbers are positive But i'm confused w/ my original problem
mathteacher1729
  • 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
  • anonymous
right but there is 1*32,2*16,4*8
mathteacher1729
  • 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
  • anonymous
okay is it 4 and 8
mathteacher1729
  • mathteacher1729
In what order? And with what signs (which is + and which is - ) ?
anonymous
  • anonymous
(7b-4)(b+8)
mathteacher1729
  • mathteacher1729
Let's factor that out now: (7b-4)(b+8) 7b^2 (good) -4b +56b = 52b (nope) 8 * -4 = -32 (good)
mathteacher1729
  • mathteacher1729
You are VERY close though!
anonymous
  • anonymous
i don't know where to go from there
anonymous
  • anonymous
i'm stuck
anonymous
  • anonymous
is it (7b-1)(b+2) ?
mathteacher1729
  • 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
  • anonymous
what do u mean?
mathteacher1729
  • mathteacher1729
(7b )(b ) Fill in the blanks with 4 and 8. One of the combinations will work. :)
mathteacher1729
  • 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
  • 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
  • anonymous
okay thank you!

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