Use the Rational Roots Test to Find All Possible Roots f(x)=54x^3+63x^2-39x-18

$f (x) = 54 x^{3} + 63 x^{2} - 39 x - 18$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18$

$q = \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18, \pm 27, \pm 54$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}, \pm \frac{1}{9}, \pm \frac{1}{18}, \pm \frac{1}{27}, \pm \frac{1}{54}, \pm 2, \pm \frac{2}{3}, \pm \frac{2}{9}, \pm \frac{2}{27}, \pm 3, \pm \frac{3}{2}, \pm 6, \pm 9, \pm \frac{9}{2}, \pm 18$

Use the Rational Roots Test to Find All Possible Roots f(x)=54x^3+63x^2-39x-18

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