Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 12$$
A) $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12$
B) $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 12 }$
C) $\pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 12 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12$
D) $\pm \frac { 1 } { 12 } , \pm 1 , \pm 12$

Question

Quizplus · Accepted Answer

The Rational Zero Theorem states that any rational zero of a polynomial is a factor of the constant term divided by a factor of the leading coefficient. Here, the constant term is -12 and the leading coefficient is 1, so the possible rational zeros are the factors of -12: $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12$.

Use the Rational Zero Theorem to List All Possible Rational f(x)=x4+5x3−5x2+4x−12f ( x ) = x ^ { 4 } + 5 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 12f(x)=x4+5x3−5x2+4x−12

Use the Rational Zero Theorem to List All Possible Rational $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 12$