3
QuizMultiple Choice

Partial Fractions — Quiz

Question 3 • Precalculus

Which sum represents the partial fraction decomposition of the fraction with numerator 8 x to the 4th power plus 3 x cubed minus 115 x squared minus 39 x plus 200 and denominator 3 x open paren x squared plus 10 close paren squared ?

Answer
A
cap A over x plus the fraction with numerator cap b x plus cap c and denominator x squared plus 10 plus the fraction with numerator cap d x plus cap e and denominator open paren x squared plus 10 close paren squared
B
cap A over 3 x plus the fraction with numerator cap b and denominator x squared plus 10
C
cap A over 3 x plus the fraction with numerator cap b x plus cap c and denominator x squared plus 10
D
cap A over x plus the fraction with numerator cap b and denominator x squared plus 10 plus the fraction with numerator cap c and denominator open paren x squared plus 10 close paren squared

Explanation

The denominator has a linear factor, x, and a repeated irreducible quadratic factor, (x² + 10)². The partial fraction form uses a constant numerator over x, then a linear numerator over each power of the quadratic: A/x + (Bx + C)/(x² + 10) + (Dx + E)/(x² + 10)². The factor 3 can be absorbed into the unknown coefficients, so choice A has the correct form.

AI-written and checked against the verified answer.

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