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

Question

1540 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-16T10:26:36

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

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)#