## College Algebra 7th Edition

$a_{0},\ \quad a_{n}$ $\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\displaystyle \pm\frac{2}{3},\pm 5,\pm\frac{5}{2},\pm\frac{5}{3},\pm\frac{5}{6},\pm 10,\pm\frac{10}{3}$
This is the Rational Zeros Theorem: ... every rational zero of $P$ is of the form $\displaystyle \frac{p}{q}$ where $p$ and $q$ are integers and $p$ is a factor of the constant coefficient $a_{0}$ $q$ is a factor of the leading coefficient $a_{n}$ In $P(x)=6x^{3}+5x^{2}-19x-10,\quad a_{0}=-10,\quad a_{n}=6$ candidates for p: $\pm 1,\pm 2,\pm 5,\pm 10$ candidates for q: $\pm 1,\pm 2,\pm 3,\pm 6$ Possible rational roots: $\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\displaystyle \pm\frac{2}{3},\pm 5,\pm\frac{5}{2},\pm\frac{5}{3},\pm\frac{5}{6},\pm 10,\pm\frac{10}{3}$