Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$
A) $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$
B) $x ^ { 3 } - 12 x + 27$
C) $x ^ { 2 } - 12 x - 27$
D) $x ^ { 3 } + 3 x ^ { 2 } + - 9 x + 27$
E) $x ^ { 3 } - 3 - x ^ { 2 } + 9 x - 27$

Question

Quizplus · Accepted Answer

The expression $(x^4 - 81) \div (x - 3)$ simplifies to $x^3 + 3x^2 + 9x + 27$, using polynomial long division or synthetic division. The divisor $x - 3$ is a factor of the dividend $x^4 - 81$, which is a difference of squares and can be factored further.

Perform the Division (x4−81)÷(x−3)\left( x ^ { 4 } - 81 \right) \div ( x - 3 )(x4−81)÷(x−3)

Perform the Division $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$