Precalculus Examples

x^{2} - 5 x + 6

$x^{2} - 5 x + 6$

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 3, \pm 6

$p = \pm 1, \pm 2, \pm 3, \pm 6$

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 3, \pm 6

$\pm 1, \pm 2, \pm 3, \pm 6$

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