Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 330: 68

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

$P(x)=x^4+8x^2+16$, a. Factor the polynomial into linear and irreducible quadratic factors: since the polynomial is a perfect square, that is $(a+b)(a+b)=a^2+2ab+b^2$, we can factor $P$ as follows: $P(x)=(x^2+4)(x^2+4)=(x^2+4)^2$. b. Factor the polynomial $P$ completely: $x^2+4=0\Rightarrow x=\pm 2i$ $P(x)=(x+2i)^2(x-2i)^2$