Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 330: 70

a. $P(x)=x(x-2)(x+2)(x^2+4)$ b. $P(x)=x(x-2)(x+2)(x-2i)(x+2i)$

$P(x)=x^5-16x$, a) Factor the polynomial into linear and irreducible quadratic factors with real coefficients: $P(x)=x(x^4-16)=x(x^2-4)(x^2+4)=x(x-2)(x+2)(x^2+4)$ b. Factor $P$ completely: $x^2+4=0\Rightarrow x=\pm 2i$ $P(x)=x(x-2)(x+2)(x-2i)(x+2i)$