List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = - 2 x ^ { 3 } + 4 x ^ { 2 } - 3 x + 8$$
A) $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$
B) $\pm \frac { 1 } { 8 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$
C) $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4$
D) $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$

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 in its lowest terms, is of the form ±(factor of the constant term)/(factor of the leading coefficient). For the given polynomial, the constant term is 8 and the leading coefficient is -2. The factors of 8 are 1, 2, 4, 8, and the factors of 2 are 1, 2. Therefore, the potential rational zeros are ±1/1, ±2/1, ±4/1, ±8/1, ±1/2. Simplifying these gives the options ±1/2, ±1, ±2, ±4, ±8.

List the Potential Rational Zeros of the Polynomial Function f(x)=−2x3+4x2−3x+8f ( x ) = - 2 x ^ { 3 } + 4 x ^ { 2 } - 3 x + 8f(x)=−2x3+4x2−3x+8

List the Potential Rational Zeros of the Polynomial Function $f ( x ) = - 2 x ^ { 3 } + 4 x ^ { 2 } - 3 x + 8$