Chapter 3, Polynomial and Rational Functions - Section 3.3 - Dividing Polynomials - 3.3 Exercises - Page 309: 2

(a) root (b) $k$

(a) If you divide $P(x)$ by $x-c$ and the remainder is $0$, then $c$ is a root of $P(x)$. (b) The Remainder Theorem states that f $P(x)$ is divided by $x-c$, the remainder is equal to $P(c)$. Thus, if $k$ is the remainder when $P(x)$ is divided by $x-c$, then $P(c)=k$.