Use the Rational Roots Test to Find All Possible Roots x^4-8x^3+11x^2+40x-80

$x^{4} - 8 x^{3} + 11 x^{2} + 40 x - 80$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 5, \pm 8, \pm 10, \pm 16, \pm 20, \pm 40, \pm 80$

$q = \pm 1$

Step 2

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

$\pm 1, \pm 2, \pm 4, \pm 5, \pm 8, \pm 10, \pm 16, \pm 20, \pm 40, \pm 80$

Use the Rational Roots Test to Find All Possible Roots x^4-8x^3+11x^2+40x-80

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