Determine all possible rational solutions of the polynomial equation.
-$$f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$$
A) $\pm 1 , \pm 2 , \pm 4 , \pm 8$
B) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8$
C) $\pm 1 , \pm 2 , \pm 4$
D) $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2$

Question

Quizplus · Accepted Answer

The Rational Root Theorem states that any rational solution of the polynomial equation $f(x) = 2x^3 + 8x^2 + 12x - 8$, in the form of $\frac{p}{q}$, must have $p$ as a factor of the constant term (-8) and $q$ as a factor of the leading coefficient (2). The factors of -8 are $\pm 1, \pm 2, \pm 4, \pm 8$, and the factors of 2 are $\pm 1, \pm 2$. Therefore, the possible rational solutions include $\pm 1, \pm \frac{1}{2}, \pm 2, \pm 4, \pm 8$.

Determine All Possible Rational Solutions of the Polynomial Equation f(x)=2x3+8x2+12x−8f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8f(x)=2x3+8x2+12x−8

Determine All Possible Rational Solutions of the Polynomial Equation $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$