Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 330: 65

$(x-5)(x-2i)(x+2i)$

$P(x)=x^3-5x^2+4x-20$ a) Factor the polynomial into linear and irreducible quadratic factors: $P(x)=x^2(x-5)+4(x-5)=(x^2+4)(x-5)$. b) Factor $P$ completely into linear factors: $x^2+4=0\Rightarrow x=\pm 2i$ $P(x)=(x-5)(x-2i)(x+2i)$