For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$$P ( x ) = 2 x ^ { 2 } - 4 x + 5 ; \frac { 1 } { 3 }$$
A) $- \frac { 1 } { 3 }$
B) $- \frac { 35 } { 9 }$
C) $\frac { 35 } { 9 }$
D) $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

The remainder theorem states that if a polynomial $P(x)$ is divided by $x - c$, the remainder is $P(c)$. For $P(x) = 2x^2 - 4x + 5$ and $c = \frac{1}{3}$, substitute $c$ into $P(x)$ to find $P(c)$: $P\left(\frac{1}{3}\right) = 2\left(\frac{1}{3}\right)^2 - 4\left(\frac{1}{3}\right) + 5 = 2\left(\frac{1}{9}\right) - \frac{4}{3} + 5 = \frac{2}{9} - \frac{4}{3} + 5 = \frac{2}{9} - \frac{12}{9} + \frac{45}{9} = \frac{35}{9}$.

For the Given Polynomial P(x) and the Given C, Use P(x)=2x2−4x+5;13P ( x ) = 2 x ^ { 2 } - 4 x + 5 ; \frac { 1 } { 3 }P(x)=2x2−4x+5;31​

For the Given Polynomial P(x) and the Given C, Use $P ( x ) = 2 x ^ { 2 } - 4 x + 5 ; \frac { 1 } { 3 }$