Algebra Examples

$f (x) = 15 x^{4} + 28 x^{3} + 66 x^{2} + 196 x + 63$

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.

$p = \pm 1, \pm 3, \pm 7, \pm 9, \pm 21, \pm 63$

$q = \pm 1, \pm 3, \pm 5, \pm 15$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm \frac{1}{5}, \pm \frac{1}{15}, \pm 3, \pm \frac{3}{5}, \pm 7, \pm \frac{7}{3}, \pm \frac{7}{5}, \pm \frac{7}{15}, \pm 9, \pm \frac{9}{5}, \pm 21, \pm \frac{21}{5}, \pm 63, \pm \frac{63}{5}$