Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = 3 x ^ { 3 } + 49 x ^ { 2 } + 49 x + 27$$
A) $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$
B) $\pm 1 , \pm 3 , \pm 9 , \pm 27$
C) $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$
D) $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that any rational zero of a polynomial function $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$ can be expressed in 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 $f(x) = 3x^3 + 49x^2 + 49x + 27$, the constant term $a_0 = 27$ and the leading coefficient $a_n = 3$. The factors of 27 are $1, 3, 9, 27$, and the factors of 3 are $1, 3$. Therefore, the potential rational zeros are $\pm 1, \pm \frac{1}{3}, \pm 3, \pm 9, \pm 27$.

Use the Rational Zeros Theorem to Write a List of All