SOLUTION: factor 10x^2-15X^3-20X^4 ax^2n-a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor 10x^2-15X^3-20X^4 ax^2n-a      Log On


   

Question 77978This question is from textbook
: factor
10x^2-15X^3-20X^4

ax^2n-a This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
10x%5E2-15x%5E3-20x%5E4

-20x%5E4-15x%5E3%2B10x%5E2 Rearrange in descending order

5x%5E2%28-4x%5E2-3x%2B2%29 Factor out the GCF of 5x%5E2.

Now lets factor the polynomial in the parenthesis (I factored out a negative 1 also):

ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .


This means that we cannot reduce %28-4x%5E2-3x%2B2%29 any further
So the polynomial 10x%5E2-15x%5E3-20x%5E4 factors to
5x%5E2%28-4x%5E2-3x%2B2%29



ax%5E%282n%29-a
a%28x%5E%282n%29-1%29 Factor out the GCF of a.
a%28x%5En%2B1%29%28x%5En-1%29 Factor using difference of squares. Notice if we foil we get
a%28x%5En%2B1%29%28x%5En-1%29=a%28x%5E%28n%2Bn%29%2Bx%5En-x%5En-1%29=a%28x%5E%282n%29-1%29

So the expression ax%5E%282n%29-a factors to
a%28x%5En%2B1%29%28x%5En-1%29