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Worksheet: Factoring the Sum and Difference of Two Cubes

Q1:

The expression ๐‘ฅ + 2 7 3 has two factors. One factor is ( ๐‘ฅ + 3 ) . What is the other factor?

  • A ๏€น ๐‘ฅ โˆ’ 9 ๐‘ฅ + 2 7 ๏… 2
  • B ๏€น ๐‘ฅ + 3 ๐‘ฅ + 9 ๏… 2
  • C ๏€น ๐‘ฅ + 3 ๐‘ฅ โˆ’ 9 ๏… 2
  • D ๏€น ๐‘ฅ โˆ’ 3 ๐‘ฅ + 9 ๏… 2
  • E ๏€น ๐‘ฅ โˆ’ 3 ๐‘ฅ + 2 7 ๏… 3

Q2:

The expression ๐‘ฅ + 6 4 3 has two factors. One factor is ( ๐‘ฅ + 4 ) . What is the other factor?

  • A ๏€น ๐‘ฅ โˆ’ 1 6 ๐‘ฅ + 6 4 ๏… 2
  • B ๏€น ๐‘ฅ + 4 ๐‘ฅ + 1 6 ๏… 2
  • C ๏€น ๐‘ฅ + 4 ๐‘ฅ โˆ’ 1 6 ๏… 2
  • D ๏€น ๐‘ฅ โˆ’ 4 ๐‘ฅ + 1 6 ๏… 2
  • E ๏€น ๐‘ฅ โˆ’ 4 ๐‘ฅ + 6 4 ๏… 3

Q3:

The expression ๐‘ฅ โˆ’ 6 4 3 has two factors. One factor is ๏€น ๐‘ฅ + 4 ๐‘ฅ + 1 6 ๏… 2 . What is the other factor?

  • A ( ๐‘ฅ + 1 6 )
  • B ( ๐‘ฅ + 4 )
  • C ( ๐‘ฅ โˆ’ 1 6 )
  • D ( ๐‘ฅ โˆ’ 4 )
  • E ๏€น ๐‘ฅ + 1 6 ๏… 2

Q4:

The expression ๐‘ฅ โˆ’ 2 1 6 3 has two factors. One factor is ๏€น ๐‘ฅ + 6 ๐‘ฅ + 3 6 ๏… 2 . What is the other factor?

  • A ( ๐‘ฅ + 3 6 )
  • B ( ๐‘ฅ + 6 )
  • C ( ๐‘ฅ โˆ’ 3 6 )
  • D ( ๐‘ฅ โˆ’ 6 )
  • E ๏€น ๐‘ฅ + 3 6 ๏… 2

Q5:

Given that ๐‘ฅ โˆ’ 5 1 2 = ( ๐‘ฅ โˆ’ 8 ) ๏€น ๐‘ฅ + ๐‘˜ + 6 4 ๏… 3 2 , find an expression for ๐‘˜ .

  • A 1 6 ๐‘ฅ
  • B โˆ’ 8 ๐‘ฅ
  • C โˆ’ 6 4 ๐‘ฅ
  • D 8 ๐‘ฅ
  • E โˆ’ 1 6 ๐‘ฅ

Q6:

Completely factor .

  • A
  • B
  • C
  • D

Q7:

Completely factor .

  • A
  • B
  • C
  • D

Q8:

Completely factor .

  • A
  • B
  • C
  • D

Q9:

Complete the factoring: .

  • A
  • B
  • C
  • D

Q10:

Completely factor .

  • A
  • B
  • C
  • D

Q11:

Completely factor .

  • A
  • B
  • C
  • D

Q12:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q13:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q14:

If ๐‘ฆ + ๐‘Ž = ( ๐‘ฆ โˆ’ 3 ) ๏€น ๐‘ฆ + 3 ๐‘ฆ + 9 ๏… 3 2 , what is the value of ๐‘Ž ?

Q15:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q16:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q17:

If ๐‘ฅ + ๐‘˜ = ( ๐‘ฅ + ๐‘˜ ) ๏€น ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๐‘˜ ๏… 3 3 2 2 , what is the value of ๐‘˜ ?

Q18:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q19:

If ๐‘Ž โˆ’ ๐‘ = 4 5 3 3 and ๐‘Ž โˆ’ ๐‘ = 9 , what is the value of ๐‘Ž + ๐‘Ž ๐‘ + ๐‘ 2 2 ?

Q20:

Completely factor .

  • A
  • B
  • C
  • D

Q21:

Complete the following: = ( ๐‘ฆ + 1 5 ๐‘ฅ ) ๏€น ๐‘ฆ โˆ’ 1 5 ๐‘ฆ ๐‘ฅ + 2 2 5 ๐‘ฅ ๏… 2 2 .

  • A ๐‘ฆ โˆ’ 1 5 3
  • B ๐‘ฆ โˆ’ 2 2 5 3
  • C ๐‘ฆ + 3 3 7 5 3
  • D ๐‘ฆ + 3 3 7 5 ๐‘ฅ 3 3
  • E ๐‘ฆ + 2 2 5 ๐‘ฅ 3 3

Q22:

If ๐‘ฅ โˆ’ ๐‘ฆ = 5 5 2 2 , ๐‘ฅ โˆ’ ๐‘ฆ = โˆ’ 5 , and ๐‘ฅ โˆ’ ๐‘ฅ ๐‘ฆ + ๐‘ฆ = 4 9 2 2 , what is the value of ๐‘ฅ + ๐‘ฆ 3 3 ?

Q23:

Complete the following: 7 2 9 ๐‘ฅ + 8 = ( + ) ๏€น 8 1 ๐‘ฅ โˆ’ 1 8 ๐‘ฅ + ๏… 3 2 .

  • A 9 ๐‘ฅ 4 4 , ,
  • B 9 ๐‘ฅ 1 8 , ,
  • C 1 8 ๐‘ฅ 4 4 , ,
  • D 9 ๐‘ฅ 2 4 , ,
  • E 9 ๐‘ฅ 4 8 , ,

Q24:

What is the result of ๏€น 2 7 ๐‘ฅ โˆ’ 1 ๏… รท ( 3 ๐‘ฅ โˆ’ 1 ) 3 , where 3 ๐‘ฅ โ‰  1 ?

  • A 9 ๐‘ฅ โˆ’ 3 ๐‘ฅ + 1 2
  • B 9 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 1 2
  • C ( 3 ๐‘ฅ โˆ’ 1 ) 2
  • D 9 ๐‘ฅ + 3 ๐‘ฅ + 1 2
  • E 9 ๐‘ฅ + 1 2

Q25:

Completely factor .

  • A
  • B
  • C
  • D
  • E