Provide an Appropriate Response $6 x - 7 = A ( 3 x - 4 ) + B ( x + 7 ) + C ( x + 7 )$

question 22

Multiple Choice

Provide an appropriate response.
-Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression $6 x - 7 = A ( 3 x - 4 ) + B ( x + 7 ) + C ( x + 7 )$ . From this equation, what can you say about the original expression?

• A) The original expression has a repeating linear factor in the denominator.
• B) The original expression has a non-reducible quadratic factor in the denominator.
• C) The original expression has a numerator of \(( 6 x - 7 ) ( 3 x - 4 ) ( x + 7 ) ( x + 7 )\).
• D) The original expression has the factor \(\left( x ^ { 2 } + 7 \right)\) in the denominator.