Use the Rational Roots Test to Find All Possible Roots 8x^4-4x^3-4x^2+x+42

$8 x^{4} - 4 x^{3} - 4 x^{2} + x + 42$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 6, \pm 7, \pm 14, \pm 21, \pm 42$

$q = \pm 1, \pm 2, \pm 4, \pm 8$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{4}, \pm \frac{1}{8}, \pm 2, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm \frac{3}{8}, \pm 6, \pm 7, \pm \frac{7}{2}, \pm \frac{7}{4}, \pm \frac{7}{8}, \pm 14, \pm 21, \pm \frac{21}{2}, \pm \frac{21}{4}, \pm \frac{21}{8}, \pm 42$

Use the Rational Roots Test to Find All Possible Roots 8x^4-4x^3-4x^2+x+42

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