Use the Rational Roots Test to Find All Possible Roots f(x)=3x^3-11x^2-35x+75

$f (x) = 3 x^{3} - 11 x^{2} - 35 x + 75$

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.

$p = \pm 1, \pm 3, \pm 5, \pm 15, \pm 25, \pm 75$

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 3, \pm 5, \pm \frac{5}{3}, \pm 15, \pm 25, \pm \frac{25}{3}, \pm 75$

Use the Rational Roots Test to Find All Possible Roots f(x)=3x^3-11x^2-35x+75

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