Chapter 3, Polynomial and Rational Functions - Chapter 3 Review - Concept Check - Page 355: 7

See the explanation

a. The remainder theorem states that when a polynomial $p(x)$ is divided by a linear polynomial $(x - a)$, then the remainder is equal to $p(a)$. b. The factor theorem states that if $f(x)$ is a polynomial of degree $n$ greater than or equal to $1$, and $a$ is any real number, then $(x - a)$ is a factor of $f(x)$ if $f(a) = 0$. c. The Rational Zero Theorem states that, if the polynomial $f(x)=a_{n}x^{n}+a_{n−1}x^{n−1}+...+a_{1}x+a_{0}$ has integer coefficients, then every rational zero of $f(x)$ has the form $p/q$ where $p$ is a factor of the constant term $a_{0}$ and $q$ is a factor of the leading coefficient $a_{n}$. When the leading coefficient is $1$, the possible rational zeros are the factors of the constant term.