Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$$
A) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$
B) $\pm 1 , \pm 2 , \pm 13 , \pm 26$
C) $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$
D) $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that potential rational zeros are the factors of the constant term divided by the factors of the leading coefficient. Here, the constant term is -26 and the leading coefficient is 13. The factors of -26 are ±1, ±2, ±13, ±26, and the factors of 13 are ±1, ±13. Thus, the potential rational zeros are ±1, ±2, ±13, ±26, ±1/13, ±2/13.

Use the Rational Zeros Theorem to Write a List of All