Worksheet: Partial Fractions: Nonrepeated Irreducible Quadratic Factors

In this worksheet, we will practice decomposing rational expressions into partial fractions when the denominator has nonrepeated irreducible quadratic factors.


Express 3𝑥+1(𝑥+4)(𝑥3) in partial fractions.

  • A21𝑥67169(𝑥+4)21169(𝑥3)+1013(𝑥3)
  • B21𝑥67169(𝑥+4)+1013(𝑥3)
  • C21𝑥67169(𝑥+4)+21169(𝑥3)+1013(𝑥3)
  • D21𝑥67169(𝑥+4)10169(𝑥3)+2113(𝑥3)
  • E21𝑥67169(𝑥+4)+10169(𝑥3)+2113(𝑥3)


The expression 3𝑥2(𝑥+4)(𝑥3) can be written in the form 𝐴𝑥+𝐵𝑥+4+𝐶𝑥3. Find the values of 𝐴, 𝐵, and 𝐶.

  • A𝐴=113, 𝐵=1013, 𝐶=113
  • B𝐴=713, 𝐵=1813, 𝐶=713
  • C𝐴=113, 𝐵=1013, 𝐶=113
  • D𝐴=713, 𝐵=1013, 𝐶=713
  • E𝐴=1813, 𝐵=713, 𝐶=113


Express 𝑥3(𝑥+2)(𝑥1) in partial fractions.

  • A𝑥+13(𝑥+2)13(𝑥1)
  • B23(𝑥+2)5𝑥+53(𝑥1)
  • C5𝑥+53(𝑥+2)23(𝑥1)
  • D5𝑥+13(𝑥+2)23(𝑥1)
  • E5𝑥+53(𝑥+2)13(𝑥1)


Decompose the following to partial fractions: 𝑥+1𝑥+8.

  • A47𝑥12(𝑥+2𝑥4)+512(𝑥+2)
  • B7𝑥412(𝑥+2𝑥4)+512(𝑥+2)
  • C47𝑥12(𝑥2𝑥+4)+512(𝑥+2)
  • D7𝑥412(𝑥2𝑥+4)+512(𝑥+2)
  • E7𝑥4(𝑥2𝑥+4)+5(𝑥+2)

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