Find the indicated value of the polynomial using the Remainder Theorem. $P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ ; find $p ( - 2 )$
A) $- 2$
B) $- 47$
C) $73$
D) $- 73$
E) $2$

Question

Quizplus · Accepted Answer

According to the Remainder Theorem, if we divide the polynomial $P(x)$ by $(x-a)$, then the remainder is $P(a)$. In this case, $a=-2$, so we divide $P(x)$ by $(x+2)$ using synthetic division:

\begin{array}{c|ccccc}
-2 & 2 & 0 & 3 & -2 & 1 \
\hline
& & -4 & 8 & -22 & 48 \
\hline
2 & 0 & 3 & 1 & -24 & \boxed{-47} \
\end{array}

Therefore, the remainder when we divide $P(x)$ by $(x+2)$ is $-47$, which is the value of $P(-2)$. So the answer is B.

Find the Indicated Value of the Polynomial Using the Remainder P(x)=2x5+3x2−2x+1P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1P(x)=2x5+3x2−2x+1

Find the Indicated Value of the Polynomial Using the Remainder $P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$