Determine all possible rational solutions of the polynomial equation.
-$$f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } + 2 x - 3$$
A) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 3 , \pm \frac { 3 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 }$
B) $\pm 1 , \pm \frac { 1 } { 2 } , \pm 3 , \pm \frac { 2 } { 3 } , \pm \frac { 1 } { 6 }$
C) $\pm 1 , \pm \frac { 1 } { 3 } , \pm 2 , \pm \frac { 2 } { 3 } , \pm 3 , \pm 6$
D) $\pm 1 , \pm 3 , \pm \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The Rational Root Theorem states that any rational solution of the polynomial equation $f(x) = 6x^3 + 24x^2 + 2x - 3$, in the form of $\frac{p}{q}$, must have $p$ as a factor of the constant term (-3) and $q$ as a factor of the leading coefficient (6). The factors of -3 are $\pm 1, \pm 3$, and the factors of 6 are $\pm 1, \pm 2, \pm 3, \pm 6$. Therefore, the possible rational solutions are $\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}$.

Determine All Possible Rational Solutions of the Polynomial Equation f(x)=6x3+24x2+2x−3f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } + 2 x - 3f(x)=6x3+24x2+2x−3

Determine All Possible Rational Solutions of the Polynomial Equation $f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } + 2 x - 3$