Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$$
A) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$
B) $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$
C) $\pm 1 , \pm 2 , \pm 13 , \pm 26$
D) $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$

Question

Quizplus · Accepted Answer

The possible rational zeros of a polynomial are given by 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. Therefore, the possible rational zeros are ±1, ±2, ±13, ±26, ±1/13, ±2/13.

Give All Possible Rational Zeros for the Following Polynomial P(x)=13x3+23x2+2x−26P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26P(x)=13x3+23x2+2x−26

Give All Possible Rational Zeros for the Following Polynomial $P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$