Use synthetic division to find the quotient and the remainder. $\frac { 4 x ^ { 4 } + 16 x ^ { 3 } + 24 x ^ { 2 } + 16 x + 4 } { x + 1 }$
A) $\text { quotient: } 4 x ^ { 3 } + 20 x ^ { 2 } + 12 x + 4 \text {; remainder: } 0$
B) $\text { quotient: } 4 x ^ { 3 } + 12 x ^ { 2 } + 12 x + 4 \text {; remainder: } 0$
C) $\text { quotient: } 4 x ^ { 3 } + 4 x ^ { 2 } + 12 x - 12 \text {; remainder: } 3$
D) $\text { quotient: } 4 x ^ { 3 } + 12 x ^ { 2 } + 12 x + 4 \text {; remainder: } 3$
E) $\text { quotient: } 4 x ^ { 3 } - 12 x ^ { 2 } + 4 x + 12 \text {; remainder: } 0$

Question

Quizplus · Accepted Answer

The synthetic division table will be as follows:

\begin{array}{c|ccccc} -1 & 4 & 16 & 24 & 16 & 4 \ \hline & & -4 & -12 & -12 & -4  \ & 4 & 12 & 12 & 4 & \ \end{array}

Therefore, the quotient is $4x^3 + 12x^2 + 12x + 4$, and the remainder is $0$. Option $(B)$ is the correct answer.

Use Synthetic Division to Find the Quotient and the Remainder 4x4+16x3+24x2+16x+4x+1\frac { 4 x ^ { 4 } + 16 x ^ { 3 } + 24 x ^ { 2 } + 16 x + 4 } { x + 1 }x+14x4+16x3+24x2+16x+4​

Use Synthetic Division to Find the Quotient and the Remainder $\frac { 4 x ^ { 4 } + 16 x ^ { 3 } + 24 x ^ { 2 } + 16 x + 4 } { x + 1 }$