Find all rational zeros of the polynomial function.
-$$f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8$$
A) $- 1 , \frac { 2 } { 3 } , 2 , - 2$
B) $1 , \frac { 2 } { 3 } , 2 , - 2$
C) $- 1 , - \frac { 2 } { 3 } , 2 , - 2$
D) $1 , - \frac { 2 } { 3 } , 2 , - 2$

Question

Quizplus · Accepted Answer

The rational root theorem can be used to find the rational zeros of the polynomial. The possible rational zeros are the factors of the constant term (-8) divided by the factors of the leading coefficient (3). Testing these possible zeros, we find that $-1$, $-\frac{2}{3}$, $2$, and $-2$ are indeed zeros of the polynomial.

Find All Rational Zeros of the Polynomial Function f(x)=3x4+5x3−10x2−20x−8f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8f(x)=3x4+5x3−10x2−20x−8

Find All Rational Zeros of the Polynomial Function $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8$