Divide using long division.
-$$\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)$$
A) $3 x + \frac { 1 } { 9 }$
B) $3 x + 9$
C) $3 x + \frac { - 2 } { 9 x ^ { 2 } - 18 }$
D) $3 x + \frac { 2 } { 9 x ^ { 2 } - 18 }$

Question

Quizplus · Accepted Answer

The division $\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)$ simplifies to $3x + \frac{1}{9}$ because dividing each term of the polynomial by $9x^2 - 18$ results in $3x$ for the $27x^3$ term, $0$ for the $x^2$ term (since it does not divide evenly), $\frac{-54x}{9x^2-18} = 0$ when simplified, and $\frac{-2}{9x^2-18} = \frac{1}{9}$ after simplification.

Divide Using Long Division (27x3+x2−54x−2)÷(9x2−18)\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)(27x3+x2−54x−2)÷(9x2−18)

Divide Using Long Division $\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)$