Precalculus Examples

x^{3} - 4 x^{2} - 7 x + 10

$x^{3} - 4 x^{2} - 7 x + 10$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form

\frac{p}{q}

$\frac{p}{q}$ where

p

$p$ is a factor of the constant and

q

$q$ is a factor of the leading coefficient.

p = \pm 1, \pm 2, \pm 5, \pm 10

$p = \pm 1, \pm 2, \pm 5, \pm 10$

q = \pm 1

$q = \pm 1$

Step 2

Find every combination of

\pm \frac{p}{q}

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

\pm 1, \pm 2, \pm 5, \pm 10

$\pm 1, \pm 2, \pm 5, \pm 10$