How do you factor out gcf from polynomial x^3 + 15?

1 Answer
Nov 16, 2016

x^3+15=(15^(1/3) + x) (15^(2/3) - 15^(1/3) x + x^2)

Explanation:

All odd order real polynomial has at least one real root. So we expect to obtain at least one real solution to the proposal

x^3+15=(x^2 + a x + b) (x + c)

After equating coefficients we arrive at

{(15 - b c=0), (b + a c=0),( a + c=0):}

Solving for a,b,c we obtain

a=-root(3)(15), b=(root(3)(15))^2, c=root(3)(15)

so

x^3+15=(15^(1/3) + x) (15^(2/3) - 15^(1/3) x + x^2)