Finite Math Examples

$f (x) = - 11 x^{4} + 8 x^{3} + 12 x^{2} - 1 x - 18$

Step 1

Rewrite $- 1 x$ as $- x$ .

$- 11 x^{4} + 8 x^{3} + 12 x^{2} - x - 18$

Step 2

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.

$p = \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18$

$q = \pm 1, \pm 11$

Step 3

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

$\pm 1, \pm \frac{1}{11}, \pm 2, \pm \frac{2}{11}, \pm 3, \pm \frac{3}{11}, \pm 6, \pm \frac{6}{11}, \pm 9, \pm \frac{9}{11}, \pm 18, \pm \frac{18}{11}$