Algebra Examples

$f (x) = - 3 x^{3} + 50 x^{2} - 225 x + 250$

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.

$p = \pm 1, \pm 2, \pm 5, \pm 10, \pm 25, \pm 50, \pm 125, \pm 250$

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 5, \pm \frac{5}{3}, \pm 10, \pm \frac{10}{3}, \pm 25, \pm \frac{25}{3}, \pm 50, \pm \frac{50}{3}, \pm 125, \pm \frac{125}{3}, \pm 250, \pm \frac{250}{3}$