SOLUTION: Factor out the common factor of: 16x^5-12x^4+20x^3+12x^2 When I think I have it partly figured out I get confused. Thank you!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Factor out the common factor of: 16x^5-12x^4+20x^3+12x^2 When I think I have it partly figured out I get confused. Thank you!      Log On


   

Question 698684: Factor out the common factor of: 16x^5-12x^4+20x^3+12x^2
When I think I have it partly figured out I get confused.
Thank you!
Answer by Positive_EV(69) About Me  (Show Source):
You can put this solution on YOUR website!
First, break apart each term into its prime factors:

16x%5E5+=+2%2A2%2A2%2A2%2Ax%2Ax%2Ax%2Ax%2Ax
12x%5E4+=+2%2A2%2A3%2Ax%2Ax%2Ax%2Ax
20x%5E3+=+2%2A2%2A5%2Ax%2Ax%2Ax
12x%5E2+=+2%2A2%2A3%2Ax%2Ax

In order to factor, a number or variable must appear in every one of the individual terms' prime factorizations. The numbers shared by every term in the polynomial is

2%2A2%2Ax%2Ax+=+4%2Ax%5E2, which is the term that can be factored out of the expression. The expression can be factored as:

, which equals
%284%2Ax%5E2%29%2A%284%2Ax%5E3-3%2Ax%5E2%2B5%2Ax%2B3%29