Write the rational expression in lowest terms.
-$$\frac { x ^ { 3 } - 216 } { x - 6 }$$
A) $x ^ { 2 } + 6 x + 36$
B) $x - 6$
C) $x ^ { 2 } - 36$
D) $x ^ { 2 } - 6 x + 36$

Question

Quizplus · Accepted Answer

The expression $\frac { x ^ { 3 } - 216 } { x - 6 }$ simplifies by recognizing that the numerator is a difference of cubes: $x^3 - 216 = x^3 - 6^3$. The difference of cubes can be factored as $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this formula with $a = x$ and $b = 6$, we get $(x - 6)(x^2 + 6x + 36)$. Dividing this by $x - 6$ leaves $x^2 + 6x + 36$, which matches choice A.

Write the Rational Expression in Lowest Terms x3−216x−6\frac { x ^ { 3 } - 216 } { x - 6 }x−6x3−216​

Write the Rational Expression in Lowest Terms $\frac { x ^ { 3 } - 216 } { x - 6 }$