Solve the equation by first factoring the polynomial

Question

Solve the equation by first factoring the polynomial

x^3 - 8 = 0

Answer 1

you have the difference of two cubes, (a^3-b^3)

this factors into (a-b)(a^2+ab+b^2)

x^3-8=x^3-2^3

so, x^3-8=(x-2)(x^2+2x+4)

x-2=0, x=2 is one real solution

x^2+2x+4=0

use the quadratic equation

(-2±√(4-16))/2

(-2±√-12)/2

(-2±2√-3)/2

(-2±[2√3]i)/2

-1±√(3)i are the two complex solutions