Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5$$
A) $\pm 5 , \pm \frac { 1 } { 5 }$
B) $\pm 1 , \pm 5$
C) $\pm 1 , \pm \frac { 1 } { 5 }$
D) $\pm \frac { 1 } { 4 } , \pm \frac { 5 } { 4 } , \pm 5$

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that any rational zero of a polynomial function, written in the form $f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$, 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 $f(x) = x^5 - 4x^2 + 3x + 5$, the constant term $a_0$ is 5 and the leading coefficient $a_n$ is 1. The factors of 5 are $\pm 1, \pm 5$, and the factors of 1 are $\pm 1$. Therefore, the potential rational zeros are $\pm 1, \pm 5$.

Use the Rational Zeros Theorem to Determine the Potential Rational f(x)=x5−4x2+3x+5f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5f(x)=x5−4x2+3x+5

Use the Rational Zeros Theorem to Determine the Potential Rational $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5$