Use the Rational Roots Test to Find All Possible Roots f(x)=16x^4-104x^3+189x^2-54x-27

$f (x) = 16 x^{4} - 104 x^{3} + 189 x^{2} - 54 x - 27$

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.

$p = \pm 1, \pm 3, \pm 9, \pm 27$

$q = \pm 1, \pm 2, \pm 4, \pm 8, \pm 16$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{4}, \pm \frac{1}{8}, \pm \frac{1}{16}, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm \frac{3}{8}, \pm \frac{3}{16}, \pm 9, \pm \frac{9}{2}, \pm \frac{9}{4}, \pm \frac{9}{8}, \pm \frac{9}{16}, \pm 27, \pm \frac{27}{2}, \pm \frac{27}{4}, \pm \frac{27}{8}, \pm \frac{27}{16}$

Use the Rational Roots Test to Find All Possible Roots f(x)=16x^4-104x^3+189x^2-54x-27

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