SOLUTION: Hi! I've just got a few questions about how to factor polynomials completely. I'm wondering if you could help me solve the following questions, explaining each step as you go.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi! I've just got a few questions about how to factor polynomials completely. I'm wondering if you could help me solve the following questions, explaining each step as you go.       Log On


   

Question 13218: Hi! I've just got a few questions about how to factor polynomials completely.
I'm wondering if you could help me solve the following questions, explaining each step as you go. 7x*2+14x-21 and 10x*2y+8xy*2+6xy
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) Factor:
7x%5E2%2B14x-21 First, factor a 7.
7%28x%5E2%2B2x-3%29 Now factor the parentheses.
Look for two integers whose product is -3 and whose sum is 2.
Try 1 X (-3) = -3 and 1 + (-3) = -2 No, this won't do it.
Try -1 X 3 = -3 and -1 + 3 = 2 Aha!
So, x%5E2%2B2x-3+=+%28x-1%29%28x%2B3%29
Putting it all together, we get:
7x%5E2%2B14x-21+=+7%28x-1%29%28x%2B3%29
2) Factor:
10x%5E2y%2B8xy%5E2%2B6xy Factor the common factor in each term, 2xy.
2xy%285x%2B4y%2B3%29 I think that's as far as you can go with this.