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Lesson: Partial Fraction Expansion: Nonrepeated Irreducible Quadratic Factors

Worksheet • 3 Questions

Q1:

Express π‘₯ βˆ’ 3 ( π‘₯ + 2 ) ( π‘₯ βˆ’ 1 ) 2 2 in partial fractions.

  • A 5 π‘₯ + 5 3 ( π‘₯ + 2 ) βˆ’ 2 3 ( π‘₯ βˆ’ 1 ) 2
  • B π‘₯ + 1 3 ( π‘₯ + 2 ) βˆ’ 1 3 ( π‘₯ βˆ’ 1 ) 2
  • C 2 3 ( π‘₯ + 2 ) βˆ’ 5 π‘₯ + 5 3 ( π‘₯ βˆ’ 1 ) 2
  • D 5 π‘₯ + 1 3 ( π‘₯ + 2 ) βˆ’ 2 3 ( π‘₯ βˆ’ 1 ) 2
  • E 5 π‘₯ + 5 3 ( π‘₯ + 2 ) βˆ’ 1 3 ( π‘₯ βˆ’ 1 ) 2

Q2:

The expression 3 π‘₯ βˆ’ 2 ( π‘₯ + 4 ) ( π‘₯ βˆ’ 3 )  can be written in the form 𝐴 π‘₯ + 𝐡 π‘₯ + 4 + 𝐢 π‘₯ βˆ’ 3  . Find the values of 𝐴 𝐡 , , and 𝐢 .

  • A 𝐴 = βˆ’ 7 1 3 , 𝐡 = 1 8 1 3 , 𝐢 = 7 1 3
  • B 𝐴 = 1 1 3 , 𝐡 = 1 0 1 3 , 𝐢 = 1 1 3
  • C 𝐴 = βˆ’ 1 1 3 , 𝐡 = 1 0 1 3 , 𝐢 = 1 1 3
  • D 𝐴 = 1 8 1 3 , 𝐡 = βˆ’ 7 1 3 , 𝐢 = 1 1 3
  • E 𝐴 = βˆ’ 7 1 3 , 𝐡 = 1 0 1 3 , 𝐢 = 7 1 3

Q3:

Express in partial fractions.

  • A 2 1 π‘₯ βˆ’ 6 7 1 6 9 ( π‘₯ + 4 ) βˆ’ 2 1 1 6 9 ( π‘₯ βˆ’ 3 ) + 1 0 1 3 ( π‘₯ βˆ’ 3 ) 2 2
  • B 2 1 π‘₯ βˆ’ 6 7 1 6 9 ( π‘₯ + 4 ) + 2 1 1 6 9 ( π‘₯ βˆ’ 3 ) + 1 0 1 3 ( π‘₯ βˆ’ 3 ) 2 2
  • C 2 1 π‘₯ βˆ’ 6 7 1 6 9 ( π‘₯ + 4 ) βˆ’ 1 0 1 6 9 ( π‘₯ βˆ’ 3 ) + 2 1 1 3 ( π‘₯ βˆ’ 3 ) 2 2
  • D 2 1 π‘₯ βˆ’ 6 7 1 6 9 ( π‘₯ + 4 ) + 1 0 1 6 9 ( π‘₯ βˆ’ 3 ) + 2 1 1 3 ( π‘₯ βˆ’ 3 ) 2 2
  • E 2 1 π‘₯ βˆ’ 6 7 1 6 9 ( π‘₯ + 4 ) + 1 0 1 3 ( π‘₯ βˆ’ 3 ) 2 2
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