Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 2 x + 5 ; k = - 1$
A) 11
B) 9
C) 12
D) 10
E) 13

Question

Quizplus · Accepted Answer

The remainder theorem states that if a polynomial $P(x)$ is divided by $x - k$, the remainder is $P(k)$. For $P(x) = x^4 - 2x^3 + x^2 - 2x + 5$ and $k = -1$, we substitute $x = -1$ into $P(x)$ to find $P(-1)$. Calculating $P(-1) = (-1)^4 - 2(-1)^3 + (-1)^2 - 2(-1) + 5 = 1 + 2 + 1 + 2 + 5 = 11$.

Use the Remainder Theorem and Synthetic Division to Find P P(x)=x4−2x3+x2−2x+5;k=−1P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 2 x + 5 ; k = - 1P(x)=x4−2x3+x2−2x+5;k=−1

Use the Remainder Theorem and Synthetic Division to Find P $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 2 x + 5 ; k = - 1$