Use the Rational Roots Test to Find All Possible Roots -3x^3+40x^2-144x+128

$- 3 x^{3} + 40 x^{2} - 144 x + 128$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 32, \pm 64, \pm 128$

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 4, \pm \frac{4}{3}, \pm 8, \pm \frac{8}{3}, \pm 16, \pm \frac{16}{3}, \pm 32, \pm \frac{32}{3}, \pm 64, \pm \frac{64}{3}, \pm 128, \pm \frac{128}{3}$

Use the Rational Roots Test to Find All Possible Roots -3x^3+40x^2-144x+128

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