Use synthetic division to divide. $\frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 }$
A) $x ^ { 3 } - 2 x ^ { 2 } + 6 x - 24 + \frac { 18 } { x - 4 }$
B) $x ^ { 3 } - 4 x ^ { 2 } + 12 x - 48 + \frac { 198 } { x - 4 }$
C) $x ^ { 3 } + 6 x + 10 + \frac { 28 } { x - 4 }$
D) $x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 48 } { x - 4 }$
E) $x ^ { 3 } + 4 x ^ { 2 } + 12 x + 48 + \frac { 198 } { x - 4 }$

Question

Quizplus · Accepted Answer

To use synthetic division, we first set up the division with the divisor (x - 4) on the left side and the coefficients of the dividend (x^4 - 4x^2 + 6) on the top:

\begin{array}{c|cccc}
4 & 1 & 0 & -4 & 0 & 6 \
\hline
& & 4 & 16 & 48 & 192 \
\hline
1 & 4 & 12 & 44 & 48 & 198 \
\end{array}

The bottom row represents the coefficients of the quotient, so we can see that the quotient is x^3 + 4x^2 + 12x + 48. The remainder is the number in the last position, divided by the divisor. In this case, it is 198/(x-4). Therefore, the correct answer is E.

Use Synthetic Division to Divide x4−4x2+6x−4\frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 }x−4x4−4x2+6​

Use Synthetic Division to Divide $\frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 }$