Precalculus Examples

$2 x^{4} + x^{3} - 35 x^{2} - 113 x + 65$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 5, \pm 13, \pm 65$

$q = \pm 1, \pm 2$

Step 2

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm \frac{1}{2}, \pm 5, \pm \frac{5}{2}, \pm 13, \pm \frac{13}{2}, \pm 65, \pm \frac{65}{2}$