How do you factorise x cubed take one?

Answer 1

If it's (x3 -1) that you want to factorize, then find the solutions to (x3 -1) = 0.

So if P(x) is a polynomial of x, and x=a is a solution for P(x) = 0, then (x - a) is a factor of P(x).

So x = 1 solves (x3 -1) = 0, so (x - 1) is a factor. Use long division (x3 -1)/(x-1) = x2 + x + 1. Use the quadratic formula to find the roots of this: -1/2 ± i*sqrt(3)/2, which is complex. So the factorization is:

• (x3 -1) = (x - 1)( x2 + x + 1)

Multiply the polynomials together to check that your answer is correct.