Provide an appropriate response.
-Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression $5 x - 8 = A ( 3 x - 3 ) + B ( x + 4 )$. From this equation, what can you say about the original expression?
A) The denominator of the original expression is $3 x ^ { 2 } + 9 x - 12$.
B) The original expression has repeated linear factors in the denominator.
C) The original expression has a non-reducible quadratic factor in the denominator.
D) The numerator of the original expression is $3 x ^ { 2 } + 9 x - 12$.

Question

Quizplus · Accepted Answer

The given algebraic expression for partial fraction decomposition suggests that the denominator of the original expression was factored into linear factors, $3x-3$ and $x+4$, indicating that the original denominator is the product of these factors, which simplifies to $3x^2 + 9x - 12$.

Provide an Appropriate Response 5x−8=A(3x−3)+B(x+4)5 x - 8 = A ( 3 x - 3 ) + B ( x + 4 )5x−8=A(3x−3)+B(x+4)

Provide an Appropriate Response $5 x - 8 = A ( 3 x - 3 ) + B ( x + 4 )$