Algebra Examples

$f (x) = 25 x^{4} - 7 x^{2} + x + 4$

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.

$p = \pm 1, \pm 2, \pm 4$

$q = \pm 1, \pm 5, \pm 25$

Step 2

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

$\pm 1, \pm \frac{1}{5}, \pm \frac{1}{25}, \pm 2, \pm \frac{2}{5}, \pm \frac{2}{25}, \pm 4, \pm \frac{4}{5}, \pm \frac{4}{25}$