Worksheet: Factorization using the Highest Common Factor

In this worksheet, we will practice factoring algebraic expressions by identifying the highest common factor (HCF).

Q1:

Write 3 5 𝑥 + 9 1 0 in the form 3 1 0 ( 𝑎 𝑥 + 𝑏 ) .

  • A 3 1 0 3 5 𝑥 + 3
  • B 3 1 0 2 𝑥 + 9 1 0
  • C 3 5 𝑥 + 9 1 0
  • D 3 1 0 ( 2 𝑥 + 3 )
  • E 3 1 0 ( 𝑥 + 3 )

Q2:

Factor 6 𝑥 + 2 4 .

  • A 6 ( 6 𝑥 + 4 )
  • B 6 ( 𝑥 + 2 4 )
  • C 3 ( 2 𝑥 + 4 )
  • D 6 ( 𝑥 + 4 )
  • E 3 ( 2 𝑥 + 2 4 )

Q3:

Factor 2 0 1 5 𝑥 .

  • A 5 ( 4 1 5 𝑥 )
  • B 5 ( 2 0 + 3 𝑥 )
  • C 5 ( 4 + 3 𝑥 )
  • D 5 ( 4 + 3 𝑥 )
  • E 5 ( 2 0 + 3 𝑥 )

Q4:

Factor the expression 3 𝑝 𝑞 + 𝑝 completely.

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

Q5:

Factor 2 𝑎 𝑏 + 8 𝑎 completely.

  • A 2 𝑎 ( 2 𝑏 + 4 )
  • B 2 𝑎 ( 𝑏 + 8 )
  • C 2 𝑎 ( 2 𝑏 + 8 )
  • D 2 𝑎 ( 𝑏 + 4 )
  • E 2 ( 𝑏 + 4 𝑎 )

Q6:

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

Q7:

Factor the expression 6 𝑝 + 3 𝑝 6 𝑝 𝑞 2 completely.

  • A 𝑝 ( 6 𝑝 6 𝑞 + 3 )
  • B 3 𝑝 ( 3 𝑝 3 𝑞 + 1 )
  • C 3 2 𝑝 2 𝑝 𝑞 + 𝑝 2
  • D 3 𝑝 ( 2 𝑝 2 𝑞 + 1 )
  • E 6 𝑝 ( 𝑝 𝑞 + 3 )

Q8:

Write 2 3 𝑥 + 1 6 in the form 1 6 ( 𝑎 𝑥 + 𝑏 ) .

  • A 1 6 4 𝑥 + 1 6
  • B 1 6 1 9 𝑥 + 1
  • C 1 6 1 4 𝑥 + 1
  • D 1 6 ( 4 𝑥 + 1 )
  • E 1 6 1 4 𝑥 + 1 6

Q9:

Factor 1 5 𝑒 + 1 5 𝑓 completely.

  • A 1 5 ( 1 5 𝑒 + 𝑓 )
  • B 1 5 ( 𝑒 + 1 5 𝑓 )
  • C 1 5 𝑒 ( 𝑒 + 𝑓 )
  • D 1 5 ( 𝑒 + 𝑓 )
  • E 1 5 𝑒 ( 𝑒 + 1 5 𝑓 )

Q10:

Factor 8 𝑥 + 4 0 𝑦 completely.

  • A 8 ( 𝑥 + 4 0 𝑦 )
  • B 8 ( 8 𝑥 + 5 𝑦 )
  • C 4 ( 2 𝑥 + 4 0 𝑦 )
  • D 8 ( 𝑥 + 5 𝑦 )
  • E 4 ( 𝑥 + 4 0 𝑦 )

Q11:

Factor 𝑥 + 3 6 𝑥 3 completely.

  • A 𝑥 ( 𝑥 + 6 ) ( 𝑥 6 )
  • B ( 𝑥 + 6 𝑖 ) ( 𝑥 6 𝑖 )
  • C ( 𝑥 + 6 𝑖 ) ( 𝑥 6 𝑖 ) 2
  • D 𝑥 ( 𝑥 + 6 𝑖 ) ( 𝑥 6 𝑖 )
  • E ( 𝑥 + 6 ) ( 𝑥 6 ) 2

Q12:

Factor the expression 4 𝑏 𝑐 + 2 𝑏 𝑑 completely.

  • A 2 ( 2 𝑏 𝑐 + 𝑏 𝑑 )
  • B 𝑏 ( 4 𝑐 + 2 𝑑 )
  • C 2 𝑏 𝑐 ( 2 + 𝑑 )
  • D 2 𝑏 ( 2 𝑐 + 𝑑 )
  • E 2 𝑏 ( 𝑐 + 𝑑 )

Q13:

Factor the expression 2 ( 𝑝 1 ) + 𝑥 ( 𝑝 1 ) completely.

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

Q14:

Expand 3 𝑥 ( 4 𝑦 7 𝑥 ) .

  • A 1 2 𝑥 𝑦 + 2 1 𝑥 2
  • B 1 2 𝑥 𝑦 2 1 𝑥 2
  • C 1 2 𝑦 + 2 1 𝑥
  • D 1 2 𝑥 𝑦 + 2 1 𝑥 2
  • E 1 2 𝑥 𝑦 2 1 𝑥

Q15:

Expand 4 7 3 4 + 8 9 𝑥 .

  • A 5 9 6 3 𝑥
  • B 3 7 + 8 9 𝑥
  • C 8 3 6 3 𝑥
  • D 3 7 + 3 2 6 3 𝑥
  • E 3 4 + 3 2 6 3 𝑥

Q16:

Which of the following expressions is equivalent to 2 ( 4 𝑥 2 ) ?

  • A 4 𝑥
  • B 8 𝑥 2
  • C 8 𝑥 + 4
  • D 8 𝑥 4
  • E 8 𝑥 + 2

Q17:

Expand 7 ( 8 1 2 𝑥 ) .

  • A 5 6 8 4 𝑥
  • B 5 6 1 2 𝑥
  • C 5 6 + 1 2 𝑥
  • D 5 6 + 8 4 𝑥
  • E 5 6 8 4 𝑥

Q18:

Which of the following expressions is equivalent to 4 ( 3 𝑥 + 2 ) ?

  • A 1 4 𝑥
  • B 1 2 𝑥 + 2
  • C 2 0 𝑥
  • D 1 2 𝑥 + 8
  • E 3 𝑥 + 8

Q19:

Which of the following expressions is equivalent to 1 1 ( 3 + 1 2 𝑥 ) ?

  • A 3 3 1 1 𝑥
  • B 3 3 + 1 3 2 𝑥
  • C 3 3 + 1 1 𝑥
  • D 3 3 1 3 2 𝑥
  • E 3 3 + 1 3 2 𝑥

Q20:

Which of the following expressions is equivalent to 9 ( 5 6 𝑥 ) ?

  • A 4 5 6 𝑥
  • B 4 5 5 4 𝑥
  • C 4 5 + 6 𝑥
  • D 4 5 + 5 4 𝑥
  • E 4 5 5 4 𝑥

Q21:

Expand 1 0 ( 3 + 5 𝑏 ) .

  • A 3 + 5 0 𝑏
  • B 3 0 + 5 𝑏
  • C 1 3 + 5 𝑏
  • D 3 0 + 5 0 𝑏
  • E 1 3 + 5 0 𝑏

Q22:

Expand 4 ( 3 + 9 𝑥 ) .

  • A 2 1 𝑥
  • B 1 2 + 9 𝑥
  • C 4 8 𝑥
  • D 1 2 + 3 6 𝑥
  • E 1 2 + 4 𝑥

Q23:

Expand 1 1 ( 5 + 7 𝑥 ) .

  • A 5 5 + 7 7 𝑥
  • B 5 5 + 7 𝑥
  • C 5 5 7 𝑥
  • D 5 5 7 7 𝑥
  • E 5 5 + 7 7 𝑥

Q24:

Expand 2 3 4 5 𝑥 3 1 0 .

  • A 8 1 5 𝑥 + 1 5
  • B 8 1 5 𝑥 3 1 0
  • C 8 1 5 𝑥 + 3 1 0
  • D 8 1 5 𝑥 1 5
  • E 4 5 𝑥 1 5

Q25:

Expand 1 2 ( 3 𝑥 + 8 ) .

  • A 4 4 𝑥
  • B 3 6 𝑥 + 8
  • C 1 3 2 𝑥
  • D 3 6 𝑥 + 9 6
  • E 1 2 𝑥 + 9 6

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