Use the Rational Roots Test to Find All Possible Roots -x^6-x^5-x^4-4x^3-12x^2+12

$- x^{6} - x^{5} - x^{4} - 4 x^{3} - 12 x^{2} + 12$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

$q = \pm 1$

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

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

Use the Rational Roots Test to Find All Possible Roots -x^6-x^5-x^4-4x^3-12x^2+12

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