For the expression the fraction with numerator 2 x squared plus 28 x plus 93 and denominator open paren x plus 6 close paren cubed , which sum represents the correct form of the partial fraction decomposition?
Answer
A
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b and denominator open paren x plus 6 close paren squared plus the fraction with numerator cap c and denominator open paren x plus 6 close paren cubed
B
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 6 close paren squared plus the fraction with numerator cap d x squared plus cap e and denominator open paren x plus 6 close paren cubed
C
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 6 close paren squared
D
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b and denominator open paren x plus 6 close paren squared
Explanation
The denominator is the repeated linear factor (x + 6)^3. For a repeated linear factor, include a fraction for each power from 1 through 3, each with a constant numerator: A/(x + 6) + B/(x + 6)^2 + C/(x + 6)^3. This is choice A.
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