Divide using synthetic division.
-$$\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$$
A) $x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 9 x + 17 + \frac { 6 } { x + 2 }$
B) $x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 17 + \frac { 6 } { x + 2 }$
C) $x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 10 x + 17 + \frac { 11 } { x + 2 }$
D) $x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 10 x - 18 + \frac { 11 } { x + 2 }$

Question

Quizplus · Accepted Answer

Synthetic division of the given polynomial by $x + 2$ (which corresponds to a root of $x = -2$) results in a quotient of $x^4 - 5x^3 + 5x^2 - 9x + 17$ and a remainder of 6, leading to the expression $x^4 - 5x^3 + 5x^2 - 9x + 17 + \frac{6}{x + 2}$.

Divide Using Synthetic Division (x5−3x4−5x3+x2−x+40)÷(x+2)\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )(x5−3x4−5x3+x2−x+40)÷(x+2)

Divide Using Synthetic Division $\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$