Write the form of the partial fraction decomposition for the following rational expression. $\frac { 4 x ^ { 2 } + 3 } { ( x + 8 ) ^ { 3 } }$
A) $\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } } + \frac { C } { ( x + 8 ) ^ { 3 } }$
B) $\frac { A x ^ { 2 } + C } { ( x + 8 ) ^ { 3 } }$
C)$\frac { A x + B } { x + 8 } + \frac { C x ^ { 2 } + D } { ( x + 8 ) ^ { 2 } } + \frac { E x ^ { 3 } + F } { ( x + 8 ) ^ { 3 } }$
D)$\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 3 } }$
E)$\frac { 3 } { x + 8 } + \frac { 4 x ^ { 2 } } { ( x + 8 ) ^ { 2 } } + \frac { A } { ( x + 8 ) ^ { 3 } }$

Question

Quizplus · Accepted Answer

The partial fraction decomposition for a denominator with a cubic term should have three terms in the form of $\frac{A}{x+a}+\frac{B}{(x+a)^2}+\frac{C}{(x+a)^3}$. Therefore, the correct choice is A.

Write the Form of the Partial Fraction Decomposition for the Following