Use the Rational Roots Test to Find All Possible Roots 3x^5-5x^2+x+6

$3 x^{5} - 5 x^{2} + x + 6$

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.

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

$q = \pm 1, \pm 3$

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 3, \pm 6$

Use the Rational Roots Test to Find All Possible Roots 3x^5-5x^2+x+6

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