Use the Rational Roots Test to Find All Possible Roots 12x^5-8x^4+36x^3-4x^2+48

$12 x^{5} - 8 x^{4} + 36 x^{3} - 4 x^{2} + 48$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 16, \pm 24, \pm 48$

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

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{4}, \pm \frac{1}{6}, \pm \frac{1}{12}, \pm 2, \pm \frac{2}{3}, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm 4, \pm \frac{4}{3}, \pm 6, \pm 8, \pm \frac{8}{3}, \pm 12, \pm 16, \pm \frac{16}{3}, \pm 24, \pm 48$

Use the Rational Roots Test to Find All Possible Roots 12x^5-8x^4+36x^3-4x^2+48

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