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 35𝑥+910 in the form 310(𝑎𝑥+𝑏).

  • A310(2𝑥+3)
  • B3102𝑥+910
  • C35𝑥+910
  • D31035𝑥+3
  • E310(𝑥+3)

Q2:

Factor 6𝑥+24.

  • A6(6𝑥+4)
  • B3(2𝑥+24)
  • C3(2𝑥+4)
  • D6(𝑥+4)
  • E6(𝑥+24)

Q3:

Factor 2015𝑥.

  • A5(4+3𝑥)
  • B5(20+3𝑥)
  • C5(4+3𝑥)
  • D5(415𝑥)
  • E5(20+3𝑥)

Q4:

Factor the expression 3𝑝𝑞+𝑝 completely.

  • A3𝑝(𝑞+1)
  • B𝑝(3𝑞+1)
  • C3𝑝(𝑞+𝑝)
  • D𝑝(3𝑞+𝑝)
  • E𝑝(𝑞+1)

Q5:

Factor 2𝑎𝑏+8𝑎 completely.

  • A2𝑎(𝑏+4)
  • B2𝑎(𝑏+8)
  • C2(𝑏+4𝑎)
  • D2𝑎(2𝑏+4)
  • E2𝑎(2𝑏+8)

Q6:

Factor the expression 3𝑝𝑛+1𝑛1 completely.

  • A𝑛+1(3𝑝+1)
  • B𝑛1(3𝑝+1)
  • C(3𝑝1)𝑛+1
  • D𝑛1(3𝑝1)
  • E𝑛(3𝑝1)+3𝑝1

Q7:

Factor the expression 6𝑝+3𝑝6𝑝𝑞 completely.

  • A3𝑝(2𝑝2𝑞+1)
  • B32𝑝2𝑝𝑞+𝑝
  • C6𝑝(𝑝𝑞+3)
  • D3𝑝(3𝑝3𝑞+1)
  • E𝑝(6𝑝6𝑞+3)

Q8:

Write 23𝑥+16 in the form 16(𝑎𝑥+𝑏).

  • A164𝑥+16
  • B1614𝑥+16
  • C1619𝑥+1
  • D16(4𝑥+1)
  • E1614𝑥+1

Q9:

Factor 15𝑒+15𝑓 completely.

  • A15(15𝑒+𝑓)
  • B15𝑒(𝑒+𝑓)
  • C15𝑒(𝑒+15𝑓)
  • D15(𝑒+15𝑓)
  • E15(𝑒+𝑓)

Q10:

Factor 8𝑥+40𝑦 completely.

  • A8(8𝑥+5𝑦)
  • B8(𝑥+5𝑦)
  • C4(2𝑥+40𝑦)
  • D4(𝑥+40𝑦)
  • E8(𝑥+40𝑦)

Q11:

Factor 𝑥+36𝑥 completely.

  • A(𝑥+6𝑖)(𝑥6𝑖)
  • B𝑥(𝑥+6𝑖)(𝑥6𝑖)
  • C(𝑥+6)(𝑥6)
  • D𝑥(𝑥+6)(𝑥6)
  • E(𝑥+6𝑖)(𝑥6𝑖)

Q12:

Factor the expression 4𝑏𝑐+2𝑏𝑑 completely.

  • A2𝑏(𝑐+𝑑)
  • B2𝑏𝑐(2+𝑑)
  • C𝑏(4𝑐+2𝑑)
  • D2(2𝑏𝑐+𝑏𝑑)
  • E2𝑏(2𝑐+𝑑)

Q13:

Factor the expression 2(𝑝1)+𝑥(𝑝1) completely.

  • A(𝑝1)(𝑥+1)
  • B𝑝(𝑥1)
  • C(𝑝1)(𝑥+2)
  • D(𝑝2)(𝑥1)
  • E(𝑝1)(2𝑥+2)

Q14:

Given that 𝑎𝑏=32, find 𝑎(𝑎𝑏)+𝑏(𝑏𝑎).

Q15:

Which of the following expressions is equivalent to 34𝑥512?

  • A34𝑥512
  • B112(9𝑥+5)
  • C14(3𝑥+5)
  • D14(3𝑥5)
  • E112(9𝑥5)

Q16:

Write a completely factored expression for the total surface area of a rectangular prism whose dimensions are 𝑙, 𝑤, and .

  • A2(𝑙𝑤+𝑙+𝑤)
  • B2(𝑤+𝑙+)
  • C2(𝑙𝑤+𝑙+𝑤)
  • D𝑙𝑤+𝑙+𝑤
  • E2𝑙(𝑤++𝑤)

Q17:

Factor 12𝑥8.

  • A4(12𝑥2)
  • B2(6𝑥8)
  • C2(6𝑥2)
  • D4(3𝑥8)
  • E4(3𝑥2)

Q18:

Find the greatest common factor of the two terms in this expression: 4𝑥18𝑥.

  • A2𝑥
  • B4𝑥
  • C18𝑥
  • D4𝑥
  • E2𝑥

Q19:

What is the greatest common factor of the expression 3𝑥𝑦11𝑥𝑦?

  • A𝑥𝑦
  • B𝑥𝑦
  • C2𝑥𝑦
  • D𝑥𝑦

Q20:

Factorize fully 24𝑥+72𝑥+54𝑥.

  • A𝑥(12𝑥+3)
  • B6𝑥(2𝑥+3)
  • C𝑥(2𝑥+3)
  • D𝑥(3𝑥+2)
  • E6𝑥(3𝑥+2)

Q21:

Factorize fully (𝑎10)(𝑎+8)2(𝑎+8).

  • A(𝑎+8)(𝑎12)
  • B(𝑎+3)(𝑎32)
  • C(𝑎+4)(𝑎24)
  • D𝑎+8𝑎12
  • E(𝑎8)(𝑎+12)

Q22:

Factorize fully 𝑥(𝑥𝑦)𝑦(𝑦𝑥) .

  • A(𝑥+𝑦)(𝑥𝑦)
  • B(𝑦+𝑥)(𝑦𝑥)
  • C(𝑥𝑦)
  • D(𝑥𝑦)(𝑦+𝑥)
  • E(𝑥+𝑦)

Q23:

Factor 15+20𝑡 completely.

  • A5(3+4𝑡)
  • B15(3+4𝑡)
  • C5(15+4𝑡)
  • D5(3+20𝑡)
  • E15(1+20𝑡)

Q24:

Using the diagram, factor 4𝑥+12.

  • A4(4𝑥+3)
  • B3(𝑥+4)
  • C4(𝑥+12)
  • D4(𝑥+3)
  • E3(4𝑥+12)

Q25:

Using the diagram, factor 6𝑥+9𝑦.

  • A3(6𝑥+3𝑦)
  • B3(2𝑥+9𝑦)
  • C6(𝑥+9𝑦)
  • D6(𝑥+3𝑦)
  • E3(2𝑥+3𝑦)

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