Precalculus Examples

$f (x) = x^{4} + x^{3} + 2 x^{3} + 4 x - 8$

Step 1

Add $x^{3}$ and $2 x^{3}$ .

$x^{4} + 3 x^{3} + 4 x - 8$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 8$

$q = \pm 1$

Step 3

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

$\pm 1, \pm 2, \pm 4, \pm 8$