Question 77978
{{{10x^2-15x^3-20x^4}}}


{{{-20x^4-15x^3+10x^2}}} Rearrange in descending order


{{{5x^2(-4x^2-3x+2)}}} Factor out the GCF of {{{5x^2}}}. 


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


*[invoke quadratic_factoring 4, 3, -2]

This means that we cannot reduce {{{(-4x^2-3x+2)}}} any further

So the polynomial {{{10x^2-15x^3-20x^4}}} factors to

{{{5x^2(-4x^2-3x+2)}}}




{{{ax^(2n)-a}}}

{{{a(x^(2n)-1)}}} Factor out the GCF of a. 

{{{a(x^n+1)(x^n-1)}}} Factor using difference of squares. Notice if we foil we get

{{{a(x^n+1)(x^n-1)=a(x^(n+n)+x^n-x^n-1)=a(x^(2n)-1)}}}


So the expression {{{ax^(2n)-a}}} factors to

{{{a(x^n+1)(x^n-1)}}}