Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }$
A) $\frac { A } { x + 8 } + \frac { B x } { ( x + 8 ) ^ { 2 } } + \frac { C x ^ { 2 } } { ( x + 8 ) ^ { 3 } }$
B) $\frac { A x + B } { x + 8 } + \frac { C x + D } { ( x + 8 ) ^ { 2 } } + \frac { E x + F } { ( x + 8 ) ^ { 3 } }$
C) $\frac { A x ^ { 2 } } { ( x + 8 ) ^ { 3 } } + \frac { B } { ( x + 8 ) ^ { 3 } }$
D) $\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } } + \frac { C } { ( x + 8 ) ^ { 3 } }$
E) $\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

For a repeated linear factor $(x + 8)^n$, the partial fraction decomposition includes terms of the form $\frac{A}{x + 8}$, $\frac{B}{(x + 8)^2}$, and $\frac{C}{(x + 8)^3}$, matching option D.

Write the Form of the Partial Fraction Decomposition of the Rational