A polynomial P is given. P(x) = x^4 + 32x^2 + 256 Find all zeros of P, real and complex and factor P completely

Answer 1

I would start out by factoring this as a first step, that helps solve for the zeros.

Factored form: (x²+16)(x²+16)

To find the zero, set each factor equal to zero and solve. Since they are both the same, this only needs to be done once.

x²+16 = 0 Subtract 16 from both sides

x² = -16 Take the square root of both sides

x = ±4i are the zeros. There are 4 complex zeros, each has a multiplicity of 2 due to the fact that the factors are the same.