Use synthetic division to perform the division. $$\frac { 3 x ^ { 3 } - 7 x ^ { 2 } - 194 x + 37 } { x + 7 }$$
A) none of these
B) $\quad 3 x ^ { 2 } - 28 x + 2$
C) $\quad 3 x ^ { 2 } - 28 x + 23 + \frac { 37 } { x + 7 }$
D) $\quad 3 x ^ { 2 } - 28 x + 2 + \frac { 23 } { x + 7 }$
E) $x ^ { 2 } - 28 x + 3 - \frac { 23 } { x + 7 }$

Question

Quizplus · Accepted Answer

Using synthetic division, we get:

$$
\begin{array}{c|cccc}
-7 & 3 & -7 & -194 & 37 \
\hline
& & -21 & 196 & -23 \
\hline
3 & -28 & - 28 & 2 & 14 \
\end{array}
$$

Therefore, our answer is $3x^2 - 28x + 2 + \frac{23}{x + 7}$. Option D is the correct choice. Notice that we added $\frac{23}{x+7}$ to our quotient because this term was left over in the remainder column after dividing by $x+7$.

Use Synthetic Division to Perform the Division 3x3−7x2−194x+37x+7\frac { 3 x ^ { 3 } - 7 x ^ { 2 } - 194 x + 37 } { x + 7 }x+73x3−7x2−194x+37​

Use Synthetic Division to Perform the Division $\frac { 3 x ^ { 3 } - 7 x ^ { 2 } - 194 x + 37 } { x + 7 }$