## College Algebra (10th Edition)

$\pm 1;\pm {3}$
In a polinomial function like $f\left( x\right) =a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots a_{1}x+a_{0}$ If $p/q$, in lowest terms, is a rational zero of $f$, then p must be a factor of $a_0$ and $q$ must be a factor of $a_n$. Here $f\left( x\right) =x^{5}-6x^{2}+9x-3\Rightarrow a_{n}=1;a_{0}=-3$ Factors of $a_0$ are $\pm 1,\pm3$ Factors of $a_n$ are $\pm1$ So the potential rational zeros are: $\pm 1;\pm {3}$