Divide using long division.
-$$\left( 2 x ^ { 4 } - 3 x ^ { 2 } + 6 x ^ { 3 } - 9 x \right) \div ( 2 x + 6 )$$
A) $x ^ { 3 } - \frac { 3 } { 2 } x$
B) $x ^ { 3 } + \frac { 3 } { 2 } x$
C) $x ^ { 3 } - 6 x + \frac { 4 x } { 2 x + 6 }$
D) $x ^ { 3 } - \frac { 3 } { 2 } x - \frac { 18 x } { 2 x + 6 }$

Question

Quizplus · Accepted Answer

First, rearrange the polynomial in descending order: $2x^4 + 6x^3 - 3x^2 - 9x$. Dividing each term by $2x + 6$ simplifies to $x^3 - \frac{3}{2}x$, as the division results in no remainder when these terms are considered.

Divide Using Long Division (2x4−3x2+6x3−9x)÷(2x+6)\left( 2 x ^ { 4 } - 3 x ^ { 2 } + 6 x ^ { 3 } - 9 x \right) \div ( 2 x + 6 )(2x4−3x2+6x3−9x)÷(2x+6)

Divide Using Long Division $\left( 2 x ^ { 4 } - 3 x ^ { 2 } + 6 x ^ { 3 } - 9 x \right) \div ( 2 x + 6 )$