Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = 6 x ^ { 4 } + 5 x ^ { 3 } - 4 x ^ { 2 } + 3 x - 5$$
A) $\pm 1 , \pm 5 , \pm \frac { 1 } { 2 } , \pm \frac { 5 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 5 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 5 } { 6 }$
B) $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm \frac { 1 } { 5 } , \pm \frac { 2 } { 5 } , \pm \frac { 3 } { 5 } , \pm \frac { 6 } { 5 }$
C) $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm \frac { 1 } { 2 } , \pm \frac { 5 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 5 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 5 } { 6 }$
D) $\pm 1 , \pm 5 , \pm \frac { 1 } { 5 } , \pm \frac { 2 } { 5 } , \pm \frac { 3 } { 5 } , \pm \frac { 6 } { 5 }$

Question

Quizplus · Accepted Answer

The Rational Zero Theorem states that any rational zero of a polynomial function will be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. For the given function, the constant term is -5 and the leading coefficient is 6. The factors of -5 are ±1, ±5, and the factors of 6 are ±1, ±2, ±3, ±6. Therefore, the possible rational zeros are ±1, ±5, ±1/2, ±5/2, ±1/3, ±5/3, ±1/6, ±5/6.

Use the Rational Zero Theorem to List All Possible Rational f(x)=6x4+5x3−4x2+3x−5f ( x ) = 6 x ^ { 4 } + 5 x ^ { 3 } - 4 x ^ { 2 } + 3 x - 5f(x)=6x4+5x3−4x2+3x−5

Use the Rational Zero Theorem to List All Possible Rational $f ( x ) = 6 x ^ { 4 } + 5 x ^ { 3 } - 4 x ^ { 2 } + 3 x - 5$