Use the Rational Roots Test to Find All Possible Roots f(x)=12x^3-67x^2+36x-5

$f (x) = 12 x^{3} - 67 x^{2} + 36 x - 5$

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.

$p = \pm 1, \pm 5$

$q = \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{4}, \pm \frac{1}{6}, \pm \frac{1}{12}, \pm 5, \pm \frac{5}{2}, \pm \frac{5}{3}, \pm \frac{5}{4}, \pm \frac{5}{6}, \pm \frac{5}{12}$

Use the Rational Roots Test to Find All Possible Roots f(x)=12x^3-67x^2+36x-5

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