Use the Rational Roots Test to Find All Possible Roots 3x^4+2x^3-6x^2-7x+10

$3 x^{4} + 2 x^{3} - 6 x^{2} - 7 x + 10$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

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

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 5, \pm \frac{5}{3}, \pm 10, \pm \frac{10}{3}$

Use the Rational Roots Test to Find All Possible Roots 3x^4+2x^3-6x^2-7x+10

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