Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4-5x^3-x^2-8x+4

$f (x) = 3 x^{4} - 5 x^{3} - x^{2} - 8 x + 4$

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.

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

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 4, \pm \frac{4}{3}$

Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4-5x^3-x^2-8x+4

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