Find the quotient and check. $\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )$
A) $12 m - 8$
B) $6 m + 2$
C) $6 m - 2$
D) $11 m + 7$
E) $9 m + 3$

Question

Quizplus · Accepted Answer

To get the quotient, we use long division as shown below:
$$
\require{enclose}
\begin{array}{c|ccccc}
\multicolumn{2}{r}{6m} & + & 2 & + & \frac{0}{9m+6} \ \cline{2-6}
9m+6 & 54m^2 & + & 54m & + & 12 \
\enclose{dotted}{6m} & & + & 6m \
\multicolumn{2}{r}{\enclose{dotted}{----------------}} & & & & \
\multicolumn{2}{r}{0} & + & 48m & + & 12 \
\multicolumn{2}{r}{} & & + & 48m & + & 32 \
\multicolumn{2}{r}{} & & & \enclose{dotted}{---------------} & & \
\multicolumn{2}{r}{} & & & 0 & &
\end{array}
$$
Therefore, the quotient is $6m+2$. We can check this by multiplying $6m+2$ by the divisor $9m+6$ using distributive property:
\begin{align*}
(6m+2)(9m+6) &= 6m(9m+6)+2(9m+6) \
&=54m^2+36m+18m+12\
&=54m^2+54m+12
\end{align*}
This is the same as the original polynomial, so our quotient must be correct.

Find the Quotient and Check (54m2+54m+12)÷(9m+6)\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )(54m2+54m+12)÷(9m+6)

Find the Quotient and Check $\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )$