Give all possible rational zeros for the following polynomial.
-$$P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24$$
A) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$
B) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$
C) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$
D) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$

Question

Quizplus · Accepted Answer

The Rational Root Theorem states that any rational zero of a polynomial $P(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$ must be of the form $\pm \frac{p}{q}$, where $p$ is a factor of the constant term $a_0$ and $q$ is a factor of the leading coefficient $a_n$. For the given polynomial, $a_0 = -24$ and $a_n = 1$, so the possible rational zeros are $\pm$ the factors of 24, which are 1, 2, 3, 4, 6, 8, 12, and 24.

Give All Possible Rational Zeros for the Following Polynomial P(x)=x3−9x2+7x−24P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24P(x)=x3−9x2+7x−24

Give All Possible Rational Zeros for the Following Polynomial $P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24$