Worksheet: Prime Factorization of Monomials

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In this worksheet, we will practice factorizing monomials completely using prime factorization.

Q1:

Which of the following is a complete factorization of 3 9 𝑥 𝑦 𝑧 ?

  • A 3 × 1 3 × 𝑥 × 𝑦 × 𝑧
  • B 1 3 × 𝑥 × 𝑦 × 𝑧
  • C 3 × 3 × 𝑥 × 𝑦 × 𝑧
  • D 3 9 × 𝑥 × 𝑦 × 𝑧
  • E 3 × 𝑥 × 𝑦 × 𝑧

Q2:

Completely factor the following expression: 3 9 𝑥 𝑦 .

  • A 1 3 ⋅ 3 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦
  • B 1 3 ⋅ 3 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦 ⋅ 𝑦
  • C 1 3 ⋅ 3 ⋅ 𝑥 ⋅ 𝑦
  • D 3 9 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦 ⋅ 𝑦
  • E 3 9 ⋅ 𝑥 ⋅ 𝑦

Q3:

List all factors of 𝑝 𝑞 .

  • A1, 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑞
  • B1, 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞
  • C 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞
  • D1, 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑞
  • E1, 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞

Q4:

Write all the factors of 3 𝑥 ?

  • A1, 3 𝑥 , 𝑥
  • B3, 𝑥 , 𝑥
  • C 3 𝑥
  • D1, 3, 𝑥
  • E1, 3, 𝑥 , 3 𝑥 , 𝑥 , 3 𝑥

Q5:

List all factors of 𝑝 𝑞 .

  • A 1 , 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑞
  • B 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞
  • C 1 , 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞
  • D 1 , 𝑝 , 𝑝 , 𝑝 𝑞 , 𝑞
  • E 1 , 𝑝 , 𝑝 𝑞 , 𝑝 𝑞 , 𝑞

Q6:

Which of the following is a complete factorization of 6 5 𝑥 𝑦 ?

  • A 5 × 5 × 𝑥 × 𝑦
  • B 6 5 × 𝑥 × 𝑦
  • C 5 × 𝑥 × 𝑦
  • D 1 3 × 𝑥 × 𝑦
  • E 5 × 1 3 × 𝑥 × 𝑦

Q7:

Which of the following is a complete factorization of 5 5 𝑥 𝑦 ?

  • A 5 5 × 𝑥 × 𝑦
  • B 5 × 1 1 × 𝑥 × 𝑦
  • C 5 × 𝑥 × 𝑦
  • D 5 × 5 × 𝑥 × 𝑦
  • E 1 1 × 𝑥 × 𝑦

Q8:

Which of the following is a complete factorization of 5 1 𝑥 𝑦 𝑧 ?

  • A 3 × 1 7 × 𝑥 × 𝑦 × 𝑧
  • B 1 7 × 𝑥 × 𝑦 × 𝑧
  • C 5 1 × 𝑥 × 𝑦 × 𝑧
  • D 3 × 𝑥 × 𝑦 × 𝑧
  • E 3 × 3 × 𝑥 × 𝑦 × 𝑧

Q9:

Completely factor the following expression: 5 1 𝑥 .

  • A 1 7 ⋅ 3 ⋅ 𝑥
  • B 1 7 ⋅ 3 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • C 5 1 ⋅ 𝑥
  • D 5 1 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • E 1 7 ⋅ 3 ⋅ 𝑥 ⋅ 𝑥

Q10:

Completely factor the following expression: 1 0 𝑥 .

  • A 2 ⋅ 5 ⋅ 𝑥 ⋅ 𝑥
  • B 1 0 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • C 2 ⋅ 5 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • D 1 0 ⋅ 𝑥
  • E 2 ⋅ 5 ⋅ 𝑥

Q11:

Completely factor the following expression: 3 8 𝑥 .

  • A 2 ⋅ 1 9 ⋅ 𝑥 ⋅ 𝑥
  • B 2 ⋅ 1 9 ⋅ 𝑥
  • C 2 ⋅ 1 9 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • D 3 8 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑥
  • E 3 8 ⋅ 𝑥

Q12:

Completely factor the following expression: 5 5 𝑥 𝑦 .

  • A 1 1 ⋅ 5 ⋅ 𝑥 ⋅ 𝑦
  • B 1 1 ⋅ 5 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦
  • C 5 5 ⋅ 𝑥 ⋅ 𝑦
  • D 5 5 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦 ⋅ 𝑦
  • E 1 1 ⋅ 5 ⋅ 𝑥 ⋅ 𝑥 ⋅ 𝑦 ⋅ 𝑦

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