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Lesson: Partial Fraction Expansion: Nonrepeated Linear Factors

Sample Question Videos

Worksheet • 5 Questions • 2 Videos

Q1:

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

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

Q2:

Find 𝐴 and 𝐡 such that 4 π‘₯ βˆ’ 2 ( π‘₯ + 3 ) ( π‘₯ βˆ’ 2 ) = 𝐴 π‘₯ + 3 + 𝐡 π‘₯ βˆ’ 2 .

  • A 𝐴 = 1 4 5 , 𝐡 = 6 5
  • B 𝐴 = βˆ’ 1 4 5 , 𝐡 = βˆ’ 6 5
  • C 𝐴 = 6 5 , 𝐡 = 1 4 5
  • D 𝐴 = βˆ’ 6 5 , 𝐡 = βˆ’ 1 4 5
  • E 𝐴 = βˆ’ 1 4 5 , 𝐡 = 6 5

Q3:

Express in partial fractions.

  • A 1 4 ( π‘₯ + 1 ) + 2 5 ( π‘₯ + 2 ) + 7 2 0 ( π‘₯ βˆ’ 3 )
  • B 1 4 ( π‘₯ + 1 ) + 2 5 ( π‘₯ + 2 ) + 1 4 ( π‘₯ βˆ’ 3 )
  • C 1 2 ( π‘₯ + 1 ) + 1 5 ( π‘₯ + 2 ) + 7 2 0 ( π‘₯ βˆ’ 3 )
  • D 1 4 ( π‘₯ + 1 ) + 2 ( π‘₯ + 2 ) + 7 2 0 ( π‘₯ βˆ’ 3 )
  • E 1 2 ( π‘₯ + 1 ) + 2 5 ( π‘₯ + 2 ) + 7 2 0 ( π‘₯ βˆ’ 3 )

Q4:

The expression 2 π‘₯ + 1 ( π‘₯ + 2 ) ( π‘₯ + 3 ) can be written in the form 𝐴 π‘₯ + 3 + 𝐡 π‘₯ + 2 . Find the values of 𝐴 and 𝐡 .

  • A 𝐴 = 5 , 𝐡 = βˆ’ 3
  • B 𝐴 = βˆ’ 5 , 𝐡 = βˆ’ 3
  • C 𝐴 = βˆ’ 3 , 𝐡 = 5
  • D 𝐴 = 5 , 𝐡 = 3
  • E 𝐴 = βˆ’ 5 , 𝐡 = 3

Q5:

Find 𝐴 and 𝐡 such that

  • A 𝐴 = 2 5 , 𝐡 = βˆ’ 2 5
  • B 𝐴 = 1 5 , 𝐡 = βˆ’ 1 5
  • C 𝐴 = βˆ’ 2 5 , 𝐡 = 2 5
  • D 𝐴 = 2 5 , 𝐡 = 2 5
  • E 𝐴 = βˆ’ 2 5 , 𝐡 = βˆ’ 2 5
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