SOLUTION: factor the following polynomial as completely as possible (((4c^4x^2-x^2-16c^4+4)))

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the following polynomial as completely as possible (((4c^4x^2-x^2-16c^4+4)))      Log On


   

Question 117697: factor the following polynomial as completely as possible
(((4c^4x^2-x^2-16c^4+4)))
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Next time, use { } instead of ( ) to express your equations.
Factor as completely as possible:
4c%5E4x%5E2+-+x%5E2+-+16c%5E4+%2B+4 Regroup the terms as shown:
4c%5E4x%5E2+-+16c%5E4+-+x%5E2+%2B+4 Now, group these into the two groups as shown, and don't forget the sign-change on the last term when add the parentheses.
%284c%5E4x%5E2+-+16c%5E4%29+-+%28x%5E2+-+4%29 Now factor each group. The first group has the common factor of 4c%5E4 while the second group has no common factor.
%284c%5E4%29%28x%5E2+-+4%29+-+%28x%5E2+-+4%29 Now you can factor the common factor of %28x%5E2+-+4%29
%28x%5E2+-+4%29%284c%5E4+-+1%29 Notice now that these two terms are both "difference of squares" binomials and these can be further factored. We'll do on set at a time.
%28x%5E2+-+4%29+=+%28x%2B2%29%28x-2%29 and...
%284c%5E4+-+1%29+=+%282c%5E2%2B1%29%282c%5E2-1%29 so...putting it all together, we get:
4c%5E4x%5E2-x%5E2-16c%5E4%2B4+=+%28x%2B2%29%28x-2%29%282c%5E2%2B1%29%282c%5E2-1%29