Perform the division. 9 x 3 − 3 x 2 − 3 x + 8 3 x + 2 \frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 } 3 x + 2 9 x 3 − 3 x 2 − 3 x + 8 A) 9 x 3 − 3 x 2 + 3 , x ≠ − 2 3 9 x ^ { 3 } - 3 x ^ { 2 } + 3 , x
eq - \frac { 2 } { 3 } 9 x 3 − 3 x 2 + 3 , x  = − 3 2 B) 3 x 2 − 3 x + 1 + 6 3 x + 2 3 x ^ { 2 } - 3 x + 1 + \frac { 6 } { 3 x + 2 } 3 x 2 − 3 x + 1 + 3 x + 2 6 C) 3 x 2 + x + 9 3 x + 2 3 x ^ { 2 } + x + \frac { 9 } { 3 x + 2 } 3 x 2 + x + 3 x + 2 9 D) 3 x 2 − x + 4 , x ≠ − 2 3 3 x ^ { 2 } - x + 4 , x
eq - \frac { 2 } { 3 } 3 x 2 − x + 4 , x  = − 3 2 E) 3 x 2 + 2 x + 3 + 7 3 x + 2 3 x ^ { 2 } + 2 x + 3 + \frac { 7 } { 3 x + 2 } 3 x 2 + 2 x + 3 + 3 x + 2 7

Question

Perform the division.   9 x 3 − 3 x 2 − 3 x + 8 3 x + 2 \frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 } 3 x + 2 9 x 3 − 3 x 2 − 3 x + 8 ​ A)    9 x 3 − 3 x 2 + 3 , x ≠ − 2 3 9 x ^ { 3 } - 3 x ^ { 2 } + 3 , x 
eq - \frac { 2 } { 3 } 9 x 3 − 3 x 2 + 3 , x  = − 3 2 ​ B)    3 x 2 − 3 x + 1 + 6 3 x + 2 3 x ^ { 2 } - 3 x + 1 + \frac { 6 } { 3 x + 2 } 3 x 2 − 3 x + 1 + 3 x + 2 6 ​ C)    3 x 2 + x + 9 3 x + 2 3 x ^ { 2 } + x + \frac { 9 } { 3 x + 2 } 3 x 2 + x + 3 x + 2 9 ​ D)    3 x 2 − x + 4 , x ≠ − 2 3 3 x ^ { 2 } - x + 4 , x 
eq - \frac { 2 } { 3 } 3 x 2 − x + 4 , x  = − 3 2 ​ E)    3 x 2 + 2 x + 3 + 7 3 x + 2 3 x ^ { 2 } + 2 x + 3 + \frac { 7 } { 3 x + 2 } 3 x 2 + 2 x + 3 + 3 x + 2 7 ​

Kohgulan Visvanathan · Accepted Answer

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

Perform the division. $9x3−3x2−3x+83x+2\frac { 9 x ^ { 3 } - 3 x ^ { 2 } - 3 x + 8 } { 3 x + 2 }$

A) $\neq - \frac { 2 } { 3 }$
B) $\frac { 6 } { 3 x + 2 }$
C) $\frac { 9 } { 3 x + 2 }$
D) $\neq - \frac { 2 } { 3 }$
E) $\frac { 7 } { 3 x + 2 }$

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