Use the Rational Roots Test to Find All Possible Roots f(x)=x^5-8x^4+21x^3-12x^2-22x+20

$f (x) = x^{5} - 8 x^{4} + 21 x^{3} - 12 x^{2} - 22 x + 20$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$

$q = \pm 1$

Step 2

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

$\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$

Use the Rational Roots Test to Find All Possible Roots f(x)=x^5-8x^4+21x^3-12x^2-22x+20

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