Factor the polynomial completely. Q(x) = x^4 − 256 Q(x) =? Find all its zeros. State the multiplicity of each zero. x=,x=,x=,x=

Answer 1

If the problem asked for the four roots of x^4 = 1, how would you answer?

You can either solve this by first factoring into (x^2 - 16)(x^2 + 16) and then into (x+4)(x-4)(x+4i)(x-4i) and say the roots are 4, -4, 4i, -4i or work from first principles and get the roots first as 4, +4, 4i, and -4i and then insert into the terms. The multiplicity of the roots is, of course, 1.

A problem that might have motivated finding the roots first would have been to factor x^8 - 256 = 0.