Use the Rational Roots Test to Find All Possible Roots 7x^5-33x^4-4x^2+3x+52

$7 x^{5} - 33 x^{4} - 4 x^{2} + 3 x + 52$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 13, \pm 26, \pm 52$

$q = \pm 1, \pm 7$

Step 2

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

$\pm 1, \pm \frac{1}{7}, \pm 2, \pm \frac{2}{7}, \pm 4, \pm \frac{4}{7}, \pm 13, \pm \frac{13}{7}, \pm 26, \pm \frac{26}{7}, \pm 52, \pm \frac{52}{7}$

Use the Rational Roots Test to Find All Possible Roots 7x^5-33x^4-4x^2+3x+52

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