Use the Rational Roots Test to Find All Possible Roots f(x)=3x^5+14x^4+22x^3+12x^2-x-2

$f (x) = 3 x^{5} + 14 x^{4} + 22 x^{3} + 12 x^{2} - x - 2$

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.

$p = \pm 1, \pm 2$

$q = \pm 1, \pm 3$

Step 2

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

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

Use the Rational Roots Test to Find All Possible Roots f(x)=3x^5+14x^4+22x^3+12x^2-x-2

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