## College Algebra (10th Edition)

$\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\pm\frac{2}{3}$
Rational Zeros Theorem Let $f$ be a polynomial function of degree 1 or higher of the form $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}\quad a_{n}\neq 0\quad a_{0}\neq 0$ where each coefficient is an integer. If $\displaystyle \frac{p}{q},$ in lowest terms, is a rational zero of $f,$ then $p$ must be a factor of $a_{0}=2,$ and $q$ must be a factor of $a_{n}=6$ . --- candidates for $p:\quad\pm 1,\pm 2$ candidates for $q:\quad\pm 1,\pm 2,\pm 3,\pm 6$ Possible zeros $\displaystyle \frac{p}{q}$ : $\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\pm\frac{2}{3}$