Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 5 } { x ^ { 3 } - 2 x ^ { 2 } }$
A) $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 3 } } + \frac { C } { x - 2 }$
B) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 2 }$
C) $\frac { A } { x } + \frac { B } { x ^ { 3 } } + \frac { C } { x ^ { 2 } - 2 }$
D) $\frac { A } { x ^ { 2 } } - \frac { B } { x ^ { 3 } } - \frac { C } { x - 2 x ^ { 2 } }$
E) $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 2 } - 2 }$

Question

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.  $\frac { 5 } { x ^ { 3 } - 2 x ^ { 2 } }$  
A) $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 3 } } + \frac { C } { x - 2 }$
B) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 2 }$
C) $\frac { A } { x } + \frac { B } { x ^ { 3 } } + \frac { C } { x ^ { 2 } - 2 }$
D) $\frac { A } { x ^ { 2 } } - \frac { B } { x ^ { 3 } } - \frac { C } { x - 2 x ^ { 2 } }$
E) $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 2 } - 2 }$

Quizplus · Accepted Answer

The denominator $x^3 - 2x^2$ can be factored as $x^2(x - 2)$, which suggests the partial fraction decomposition should include terms for $x$ and $x^2$ from the $x^2$ factor, and a term for $x - 2$.

Write the Form of the Partial Fraction Decomposition of the Rational