Perform the indicated operation.
-Use synthetic division to divide $- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20$ by $x + 4$
A) $- \frac { 1 } { 2 } x ^ { 2 } - \frac { 5 } { 2 } x - \frac { 3 } { 4 }$
B) $- 2 x ^ { 2 } - 2 x + 5$
C) $- 2 x - 2$
D) $2 x ^ { 2 } - 4 x + 5$

Question

Quizplus · Accepted Answer

To use synthetic division to divide $- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20$ by $x + 4$, we set up the division with -4 (since we divide by $x + 4$, we use the opposite sign). The coefficients of the polynomial are -2, -10, -3, and 20. Proceeding with synthetic division:-4 | -2 -10 -3  20     |____8  8 -20       -2 -2  5  0The result is $-2x^2 - 2x + 5$, and there is no remainder, indicating that $x + 4$ is a factor of the given polynomial.

Perform the Indicated Operation −2x3−10x2−3x+20- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20−2x3−10x2−3x+20

Perform the Indicated Operation $- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20$