Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 13

Remainder = $0$ $(x-2)$ 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, $f(2)=(3)(2^4)-(6)(2^3)-(5)(2)+10=(3)(16)-(6)(8)-(5)(2)+10=0$ 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 $(x-2)$ is a factor of $f(x)$ .