Decompose P/Q, Where Q Has Repeated Linear Factors
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$\frac { 48 - 8 x } { x ^ { 3 } - 8 x ^ { 2 } + 16 x }$
A) $\frac { 3 } { x } + \frac { - 3 } { x - 4 } + \frac { 4 } { ( x - 4 ) ^ { 2 } }$
B) $\frac { 3 } { x } + \frac { 4 } { x - 4 } + \frac { - 3 } { ( x - 4 ) ^ { 2 } }$
C) $\frac { 3 } { x } + \frac { - 3 } { x - 4 } + \frac { 8 } { ( x - 4 ) ^ { 2 } }$
D) $\frac { - 3 } { x } + \frac { 3 } { x - 4 } + \frac { 4 } { ( x - 4 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominator $x^3 - 8x^2 + 16x$ can be factored as $x(x-4)^2$, indicating one linear factor $x$ and a repeated linear factor $(x-4)^2$. The correct partial fraction decomposition must include terms for each of these factors: $\frac{A}{x}$, $\frac{B}{x-4}$, and $\frac{C}{(x-4)^2}$, matching option A.

Decompose P/Q, Where Q Has Repeated Linear Factors Write the Form

Decompose P/Q, Where Q Has Repeated Linear Factors
Write the Form