11
QuizMultiple Choice

Modeling with Rational and Piecewise-Defined Functions: Part One — Test

Question 11 • Precalculus

What is the correct form of the partial fraction decomposition for the fraction with numerator 6 x plus 7 and denominator open paren x plus 2 close paren squared ?

Answer
A
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b and denominator open paren x plus 2 close paren squared
B
cap A over x plus the fraction with numerator cap b and denominator x plus 2 plus the fraction with numerator cap c x plus cap d and denominator open paren x plus 2 close paren squared
C
cap A over x plus the fraction with numerator cap b and denominator x plus 2 plus the fraction with numerator cap c and denominator open paren x plus 2 close paren squared
D
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 2 close paren squared

Explanation

The denominator is the repeated linear factor (x + 2)². For a repeated linear factor, include one fraction for each power of that factor: A/(x + 2) + B/(x + 2)². This matches choice A; a linear numerator over (x + 2)² is not needed because that factor is linear.

AI-written and checked against the verified answer.

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