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

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that the potential rational zeros of a polynomial are the factors of the constant term divided by the factors of the leading coefficient. Here, the constant term is -8 and the leading coefficient is 2. The factors of -8 are ±1, ±2, ±4, ±8, and the factors of 2 are ±1, ±2. Dividing these gives the potential rational zeros: ±1, ±1/2, ±2, ±4, ±8.

Use the Rational Zeros Theorem to Write a List of All