Use the remainder theorem and synthetic division to find f(k).
-$k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3$
A) -15
B) -9
C) -1
D) 0

Question

Use the remainder theorem and synthetic division to find f(k).
-$k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3$
A)  -15 
B)  -9 
C)  -1 
D) 0

Quizplus · Accepted Answer

The remainder theorem states that if a polynomial $f(x)$ is divided by $x - k$, the remainder is $f(k)$. For $k = 1$, we perform synthetic division with 1:$$\begin{array}{r|rrrrrr}1 & 5 & 0 & 2 & -5 & 0 & -3 \\hline & \downarrow & 5 & 5 & 7 & 2 & 2 \\end{array}$$Adding the numbers in the bottom row gives the new coefficients: $5, 5, 7, 2, 2$, and the remainder is $-1$. Therefore, $f(1) = -1$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=1;f(x)=5x5+2x3−5x2−3k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3k=1;f(x)=5x5+2x3−5x2−3

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