Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 8 x - 24$$
A) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$
B) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$
C) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$
D) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that any rational zero of a polynomial is a factor of the constant term divided by a factor of the leading coefficient. Here, the constant term is -24 and the leading coefficient is 1. The factors of -24 are $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24$, and the factors of 1 are $\pm 1$. Thus, the potential rational zeros are $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24$.

Use the Rational Zeros Theorem to Write a List of All