Use the Rational Roots Test to Find All Possible Roots f(x)=x^6-4x^5+20x^4-21x^3-6x^2-37x-14

$f (x) = x^{6} - 4 x^{5} + 20 x^{4} - 21 x^{3} - 6 x^{2} - 37 x - 14$

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.

$p = \pm 1, \pm 2, \pm 7, \pm 14$

$q = \pm 1$

Step 2

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

$\pm 1, \pm 2, \pm 7, \pm 14$

Use the Rational Roots Test to Find All Possible Roots f(x)=x^6-4x^5+20x^4-21x^3-6x^2-37x-14

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