Divide the polynomials by using an appropriate method. $$\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)$$
A) $- 8 n + 3 + \frac { 3 n } { 6 n ^ { 2 } + 4 n + 1 }$
B) $- 8 n + 3 + \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$
C) $- 8 n + 3 - \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$
D) $- 8 n - 3$

Question

Quizplus · Accepted Answer

To divide the given polynomials, we use polynomial long division or synthetic division. The first term of the quotient is obtained by dividing $-48n^3$ by $6n^2$, which gives $-8n$. Multiplying the divisor by $-8n$ and subtracting from the dividend, we proceed to the next terms similarly. The final quotient is $-8n + 3$ with a remainder of $3n + 8$, which gives the correct answer as $- 8 n + 3 + \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$.

Divide the Polynomials by Using an Appropriate Method (−48n3−14n2+7n+11)÷(6n2+4n+1)\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)(−48n3−14n2+7n+11)÷(6n2+4n+1)

Divide the Polynomials by Using an Appropriate Method $\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)$