Worksheet: Factoring by Grouping

In this worksheet, we will practice factorizing expressions by grouping.

Q1:

Factorise fully 𝑥 + 𝑥 1 3 0 3 .

  • A ( 𝑥 5 ) 𝑥 5 𝑥 + 2 6 2
  • B ( 𝑥 + 5 ) 𝑥 + 5 𝑥 + 2 6 2
  • C ( 𝑥 5 ) 𝑥 + 5 𝑥 + 2 5 2
  • D ( 𝑥 5 ) 𝑥 + 5 𝑥 + 2 6 2

Q2:

Factorise fully 𝑥 2 𝑥 + 5 𝑥 1 0 3 2 .

  • A ( 𝑥 5 ) ( 𝑥 + 2 ) 2
  • B ( 𝑥 5 ) ( 𝑥 2 ) 2
  • C ( 𝑥 2 ) ( 𝑥 + 5 ) 2
  • D ( 𝑥 + 5 ) ( 𝑥 2 ) 2
  • E ( 𝑥 + 2 ) ( 𝑥 5 ) 2

Q3:

Factorise fully 𝑥 + 9 𝑥 8 𝑥 7 2 5 2 3 .

  • A 𝑥 + 8 𝑥 + 9 2 3
  • B 𝑥 8 𝑥 9 2 3
  • C ( 𝑥 8 ) 𝑥 + 9 2
  • D 𝑥 8 𝑥 + 9 2 3

Q4:

Factorise fully 𝑧 + 6 𝑧 + 6 + 𝑧 3 2 .

  • A ( 𝑧 1 ) 𝑧 + 6 2
  • B ( 𝑧 1 ) ( 𝑧 + 1 ) ( 𝑧 + 6 )
  • C 𝑧 + 1 𝑧 + 6 2 2
  • D 𝑧 + 1 ( 𝑧 + 6 ) 2
  • E ( 𝑧 + 1 ) 𝑧 + 6 2

Q5:

Factorise fully 𝑥 𝑦 2 7 𝑥 𝑦 + 2 7 2 3 2 3 .

  • A ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 + 3 ) 𝑦 3 𝑦 + 9 2
  • B ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 3 ) 𝑦 3 𝑦 + 9 2
  • C ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑦 3 2
  • D ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 3 ) 𝑦 + 3 𝑦 + 9 2
  • E ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑦 + 3 2

Q6:

Expand 𝑎 ( 𝑎 1 6 𝑏 ) + 6 4 𝑏 8 1 2 , and then factorise the result completely.

  • A ( 𝑎 8 𝑏 + 9 ) ( 𝑎 + 8 𝑏 9 )
  • B ( 𝑎 + 8 𝑏 + 9 ) ( 𝑎 + 8 𝑏 9 )
  • C ( 𝑎 8 𝑏 9 ) 2
  • D ( 𝑎 8 𝑏 + 9 ) ( 𝑎 8 𝑏 9 )
  • E ( 𝑎 + 9 𝑏 ) ( 𝑎 9 𝑏 )

Q7:

Factorise fully 𝑥 𝑥 𝑥 + 1 5 3 2 .

  • A ( 𝑥 + 1 ) ( 𝑥 1 ) 𝑥 + 𝑥 + 1 2 2
  • B ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑥 𝑥 + 1 2 2
  • C 𝑥 + 1 ( 𝑥 + 1 ) 𝑥 + 𝑥 + 1 2 2
  • D ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑥 + 𝑥 + 1 2 2
  • E 𝑥 + 1 ( 𝑥 1 ) 𝑥 + 𝑥 + 1 2 2

Q8:

Expand and simplify 𝑎 9 𝑏 + 𝑎 𝑏 ( 𝑎 9 𝑏 ) 3 3 , then factorise the result.

  • A ( 𝑎 + 𝑏 ) ( 𝑎 + 3 𝑏 ) 2
  • B ( 𝑎 𝑏 ) ( 𝑎 + 3 𝑏 ) ( 𝑎 3 𝑏 )
  • C ( 𝑎 + 𝑏 ) ( 𝑎 3 𝑏 ) 2
  • D ( 𝑎 + 𝑏 ) ( 𝑎 + 3 𝑏 ) ( 𝑎 3 𝑏 )
  • E ( 𝑎 3 𝑏 ) 3

Q9:

Factorise fully 1 𝑥 + 1 4 𝑥 𝑦 4 9 𝑦 2 2 .

  • A ( 1 + 𝑥 9 𝑦 ) ( 1 𝑥 + 9 𝑦 )
  • B ( 1 + 𝑥 7 𝑦 ) ( 1 𝑥 7 𝑦 )
  • C ( 1 + 𝑥 9 𝑦 ) ( 1 𝑥 9 𝑦 )
  • D ( 1 + 𝑥 7 𝑦 ) ( 1 𝑥 + 7 𝑦 )

Q10:

Factorise fully 𝑎 + 𝑏 + 𝑎 + 𝑏 3 3 .

  • A ( 𝑎 + 𝑏 ) 𝑎 + 𝑎 𝑏 + 𝑏 1 2 2
  • B ( 𝑎 𝑏 ) 𝑎 + 𝑎 𝑏 + 𝑏 + 1 2 2
  • C ( 𝑎 + 𝑏 ) 𝑎 𝑎 𝑏 + 𝑏 2 2
  • D ( 𝑎 + 𝑏 ) 𝑎 𝑎 𝑏 + 𝑏 + 1 2 2

Q11:

Factorise fully 𝑥 + 4 𝑥 𝑥 4 3 2 .

  • A ( 𝑥 + 4 ) ( 𝑥 1 ) 2
  • B ( 𝑥 + 1 ) ( 𝑥 1 ) ( 𝑥 4 )
  • C ( 𝑥 + 4 ) ( 𝑥 4 ) ( 𝑥 1 )
  • D ( 𝑥 + 1 ) ( 𝑥 1 ) ( 𝑥 + 4 )
  • E ( 𝑥 + 1 ) ( 𝑥 + 4 ) 2

Q12:

Factorise fully 4 𝑥 ( 𝑥 + 2 ) 1 6 𝑥 3 2 𝑥 3 2 .

  • A 4 𝑥 ( 𝑥 2 ) 𝑥 + 4 2
  • B 4 𝑥 ( 𝑥 + 2 ) ( 𝑥 2 ) 2
  • C 4 𝑥 ( 𝑥 + 2 ) 𝑥 + 4 2 2
  • D 4 𝑥 ( 𝑥 2 ) ( 𝑥 + 2 ) 2
  • E 𝑥 ( 𝑥 2 ) ( 𝑥 + 2 ) 2

Q13:

Factorise fully 𝑥 ( 𝑦 5 ) 9 𝑥 ( 𝑦 5 ) + 1 8 𝑦 9 0 2 .

  • A ( 𝑦 5 ) ( 𝑥 + 1 ) ( 𝑥 + 1 8 )
  • B ( 𝑦 5 ) ( 𝑥 + 6 ) ( 𝑥 + 3 )
  • C ( 𝑦 5 ) ( 𝑥 + 2 ) ( 𝑥 + 9 )
  • D ( 𝑦 5 ) ( 𝑥 6 ) ( 𝑥 3 )
  • E ( 𝑦 + 5 ) ( 𝑥 6 ) ( 𝑥 3 )

Q14:

Factor the expression 3 𝑝 𝑛 + 1 𝑛 1 3 3 completely.

  • A 𝑛 ( 3 𝑝 1 ) + 3 𝑝 1 3
  • B 𝑛 1 ( 3 𝑝 + 1 ) 3
  • C 𝑛 + 1 ( 3 𝑝 + 1 ) 3
  • D ( 3 𝑝 1 ) 𝑛 + 1 3
  • E 𝑛 1 ( 3 𝑝 1 ) 3

Q15:

Factor the expression 𝑥 ( 2 𝑥 + 5 ) + 2 𝑥 + 5 completely.

  • A 2 𝑥 ( 2 𝑥 + 5 )
  • B ( 2 𝑥 + 5 ) ( 𝑥 + 5 )
  • C ( 2 𝑥 + 5 ) ( 𝑥 + 2 )
  • D ( 𝑥 + 1 ) ( 2 𝑥 + 5 )
  • E 𝑥 ( 2 𝑥 + 5 )

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