Use the Rational Roots Test to Find All Possible Roots 36x^4-156x^3+229x^2-64x+5

$36 x^{4} - 156 x^{3} + 229 x^{2} - 64 x + 5$

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.

$p = \pm 1, \pm 5$

$q = \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 9, \pm 12, \pm 18, \pm 36$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{4}, \pm \frac{1}{6}, \pm \frac{1}{9}, \pm \frac{1}{12}, \pm \frac{1}{18}, \pm \frac{1}{36}, \pm 5, \pm \frac{5}{2}, \pm \frac{5}{3}, \pm \frac{5}{4}, \pm \frac{5}{6}, \pm \frac{5}{9}, \pm \frac{5}{12}, \pm \frac{5}{18}, \pm \frac{5}{36}$

Use the Rational Roots Test to Find All Possible Roots 36x^4-156x^3+229x^2-64x+5

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