Perform the division.
-$\frac { x ^ { 4 } + 81 } { x - 3 }$
A) $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27 + \frac { 162 } { x - 3 }$
B) $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$
C) $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 162 } { x - 3 }$
D) $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 81 } { x - 3 }$

Question

Quizplus · Accepted Answer

To divide $\frac { x ^ { 4 } + 81 } { x - 3 }$, we use polynomial long division or synthetic division. The quotient is $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$, and the remainder is $81 + 27(3) = 162$, giving the full expression as $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 162 } { x - 3 }$.

Perform the Division x4+81x−3\frac { x ^ { 4 } + 81 } { x - 3 }x−3x4+81​

Perform the Division $\frac { x ^ { 4 } + 81 } { x - 3 }$