SOLUTION: I have a problem with factoring. I don't know how to do it. I just need to know how to factor this problem then I think I can do the rest. The directions say solve each inequali

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Question 131978This question is from textbook College Algebra
: I have a problem with factoring. I don't know how to do it. I just need to know how to factor this problem then I think I can do the rest. The directions say solve each inequality algerbraically.
16. 25x2-40x+16<0


24. x3+2x2-3x>0
Thank you
Tara This question is from textbook College Algebra

Answer by solver91311(24713) About Me  (Show Source):
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25x%5E2-40x%2B16

Well, if each factor had a 5x and each factor had a -4, that would take care of the x%5E2 and constant terms, so let's see what happens to the middle term:

%285x-4%29%285x-4%29=25x%5E2-20x-20x%2B16=25x%5E2-40x%2B16. Yep, that does it.

x%5E3%2B2x%5E2-3x. This one has at least one x in every term, so you can start by factoring out an x.

x%28x%5E2%2B2x-3%29.

Now, 3%2A-1=-3 and 3%2B%28-1%29=2, so the rest of this thing should factor to:

x%28x-1%29%28x%2B3%29

Check by multiplying it out: x%28x-1%29%28x%2B3%29=x%28x%5E2%2B3x-x-3%29=x%28x%5E2%2B2x-3%29=x%5E3%2B2x%5E2-3x. Yep, that works.