List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14$$
A) $\pm 1 , \pm 7 , \pm 2 , \pm 14$
B) $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 }$
C) $\pm 1 , \pm 7 , \pm 2$
D) $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 } , \pm 7 , \pm 2 , \pm 14$

Question

Quizplus · Accepted Answer

The potential rational zeros of a polynomial function can be found using the Rational Root Theorem, which states that any rational zero, expressed as a fraction $\frac{p}{q}$, must have $p$ as a factor of the constant term (in this case, 14) and $q$ as a factor of the leading coefficient (in this case, 1). Therefore, the potential rational zeros are $\pm 1, \pm 2, \pm 7, \pm 14$.

List the Potential Rational Zeros of the Polynomial Function f(x)=x5−4x2+3x+14f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14f(x)=x5−4x2+3x+14

List the Potential Rational Zeros of the Polynomial Function $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14$