Factor each and find all zeros: f(x)= x^6+16x^3+64

Question

Steps on how to achieve the answer would be so helpful!

Answer 1

f(x)= x⁶+16x³+64

Let z = x³ , then the equation becomes:

z² + 16z + 64

This is (z + 8)*(z + 8)

Replace z with x³ and we have (x³ + 8)*(x³ + 8)

Set either one equal to zero, and we have:

x³ + 8 = 0

x³ = -8

x = -2 (The only zero---AKA "root")