Use synthetic division to divide. $\frac { 4 x ^ { 3 } + 20 x ^ { 2 } - 27 x - 18 } { x + \frac { 1 } { 2 } }$
A) $4 x ^ { 2 } + 18 x + 36 , x \neq - \frac { 1 } { 2 }$
B) $4 x ^ { 2 } + 18 x - 36 , x \neq - \frac { 1 } { 2 }$
C) $4 x ^ { 2 } - 18 x - 36 , x \neq - \frac { 1 } { 2 }$
D) $- 4 x ^ { 2 } + 18 x - 36 , x \neq - \frac { 1 } { 2 }$
E) $- x ^ { 2 } - 18 x - 36 , x \neq - \frac { 1 } { 2 }$

Question

Use synthetic division to divide.​ $\frac { 4 x ^ { 3 } + 20 x ^ { 2 } - 27 x - 18 } { x + \frac { 1 } { 2 } }$ ​
A) $4 x ^ { 2 } + 18 x + 36 , x \neq - \frac { 1 } { 2 }$
B) $4 x ^ { 2 } + 18 x - 36 , x \neq - \frac { 1 } { 2 }$
C)​ $4 x ^ { 2 } - 18 x - 36 , x \neq - \frac { 1 } { 2 }$
D) $- 4 x ^ { 2 } + 18 x - 36 , x \neq - \frac { 1 } { 2 }$
E) $- x ^ { 2 } - 18 x - 36 , x \neq - \frac { 1 } { 2 }$

Quizplus · Accepted Answer

To use synthetic division with $x + \frac{1}{2} = 0$, we set up the division with $-\frac{1}{2}$ and the coefficients $4, 20, -27, -18$. The process yields a quotient of $4x^2 + 18x - 36$, making option B correct.

Use Synthetic Division to Divide 4x3+20x2−27x−18x+12\frac { 4 x ^ { 3 } + 20 x ^ { 2 } - 27 x - 18 } { x + \frac { 1 } { 2 } }x+21​4x3+20x2−27x−18​

Use Synthetic Division to Divide $\frac { 4 x ^ { 3 } + 20 x ^ { 2 } - 27 x - 18 } { x + \frac { 1 } { 2 } }$