Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 3$$
A) $\pm 1 , \pm 3 , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 }$
B) $\pm 1 , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 }$
C) $\pm 1 , \pm \frac { 1 } { 3 } , \pm 2 , \pm \frac { 2 } { 3 }$
D) $\pm 1 , \pm 2 , \pm 3$

Question

Quizplus · Accepted Answer

The Rational Root Theorem states that any rational root, expressed in its lowest terms $p/q$, of a polynomial equation with integer coefficients is a factor of the constant term (in this case, -3) divided by a factor of the leading coefficient (in this case, 2). Therefore, the possible rational zeros are $\pm 1, \pm 3, \pm \frac{1}{2}, \pm \frac{3}{2}$.

Give All Possible Rational Zeros for the Following Polynomial P(x)=2x3−5x2+7x−3P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 3P(x)=2x3−5x2+7x−3

Give All Possible Rational Zeros for the Following Polynomial $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 3$