Perform the division. $\frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 }$
A) $9 x ^ { 3 } - 3 x ^ { 2 } + 3 , x \neq - \frac { 2 } { 3 }$
B) $3 x ^ { 2 } - 3 x + 1 + \frac { 6 } { 3 x + 2 }$
C) $3 x ^ { 2 } + x + \frac { 9 } { 3 x + 2 }$
D) $3 x ^ { 2 } - x + 4 , x \neq - \frac { 2 } { 3 }$
E) $3 x ^ { 2 } + 2 x + 3 + \frac { 7 } { 3 x + 2 }$

Question

Quizplus · Accepted Answer

To divide $\frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 }$, we use polynomial long division or synthetic division. The result is $3 x ^ { 2 } - 3 x + 1 + \frac { 6 } { 3 x + 2 }$, which matches option B. This is because each term of the dividend is divided by $3x + 2$, and the remainder is $6$, which cannot be divided further by $3x + 2$, hence it is written as a fraction over the divisor.

Perform the Division 9x3−3x2−3x+83x+2\frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 }3x+29x3−3x2−3x+8​

Perform the Division $\frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 }$