SOLUTION: How do you factor a polynomial with x^3? One x cannot be factored out. The equation to be factored is x^3 + 2x^2 - 16x - 32 Please help!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you factor a polynomial with x^3? One x cannot be factored out. The equation to be factored is x^3 + 2x^2 - 16x - 32 Please help!      Log On


   

Question 81600: How do you factor a polynomial with x^3?
One x cannot be factored out.
The equation to be factored is x^3 + 2x^2 - 16x - 32
Please help!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the expression:
x%5E3%2B2x%5E2-16x-32 You can use the technique known as factoring by grouping: %28x%5E3%2B2x%5E2%29-%2816x%2B32%29
Notice the change of sign in the last term. This comes about because when you add the parentheses, you are now multiplying both terms within the parenthese by -1 thus changing the sign of the last term back to a positive.
Now factor x%5E2 from the first group and factor 16 from the second group.
x%5E2%28x+%2B+2%29+-+16%28x+%2B+2%29 Now you can factor out the common factor of (x+2).
%28x%2B2%29%28x%5E2-16%29 Notice now, that the second factor (x%5E2-16) is the difference of two squares and this can be factored to give.
%28x%5E2-16%29+=+%28x%2B4%29%28x-4%29
Now put it all together to get:
%28x%2B2%29%28x%2B4%29%28x-4%29