Use the Rational Roots Test to Find All Possible Roots f(x)=4x^4+8x^3-33x^2-2x+8

$f (x) = 4 x^{4} + 8 x^{3} - 33 x^{2} - 2 x + 8$

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.

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

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

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{4}, \pm 2, \pm 4, \pm 8$

Use the Rational Roots Test to Find All Possible Roots f(x)=4x^4+8x^3-33x^2-2x+8

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