Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 16

Remainder = $0$ $(x+3)$ is a factor of $f(x)$ .

The Remainder Theorem states that when a function $f(x)$ is divided by $(x-R)$ , then the remainder will be: $f(R)$. Now, $f(-3)=(2)(-3)^6-18(-3)^4+(-3)^2-9 =(2)(729)-(18)(81)+9-9=1458-1458=0$ The Factor Theorem states that if $f(a)=0$, then $(x-a)$ is a factor of $f(x)$ and vice versa. Therefore, by the Factor Theorem $(x+3)$ is a factor of $f(x)$ .