Use the Rational Roots Test to Find All Possible Roots f(x)=x^5-9x^4+13x^3+57x^2-86x-120

$f (x) = x^{5} - 9 x^{4} + 13 x^{3} + 57 x^{2} - 86 x - 120$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15, \pm 20, \pm 24, \pm 30, \pm 40, \pm 60, \pm 120$

$q = \pm 1$

Step 2

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

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15, \pm 20, \pm 24, \pm 30, \pm 40, \pm 60, \pm 120$

Use the Rational Roots Test to Find All Possible Roots f(x)=x^5-9x^4+13x^3+57x^2-86x-120

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