Lesson Worksheet: Prime Factorization of Monomials Mathematics

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

Q1:

Which of the following is a complete factorization of 39𝑥𝑦𝑧?

  • A3×𝑥×𝑦×𝑧
  • B39×𝑥×𝑦×𝑧
  • C3×13×𝑥×𝑦×𝑧
  • D3×3×𝑥×𝑦×𝑧
  • E13×𝑥×𝑦×𝑧

Q2:

Completely factor the following expression: 39𝑥𝑦.

  • A13⋅3⋅𝑥⋅𝑥⋅𝑦⋅𝑦
  • B13⋅3⋅𝑥⋅𝑥⋅𝑦
  • C39⋅𝑥⋅𝑦
  • D39⋅𝑥⋅𝑥⋅𝑦⋅𝑦
  • E13⋅3⋅𝑥⋅𝑦

Q3:

List all factors of 𝑝𝑞.

  • A𝑝, 𝑝, 𝑝𝑞, 𝑝𝑞, 𝑞
  • B1, 𝑝, 𝑝𝑞, 𝑝𝑞, 𝑞
  • C1, 𝑝, 𝑝, 𝑝𝑞, 𝑞
  • D1, 𝑝, 𝑝, 𝑝𝑞, 𝑞
  • E1, 𝑝, 𝑝, 𝑝𝑞, 𝑝𝑞, 𝑞

Q4:

Write all the factors of 3𝑥?

  • A1, 3𝑥, 𝑥
  • B1, 3, 𝑥, 3𝑥, 𝑥, 3𝑥
  • C3, 𝑥, 𝑥
  • D1, 3, 𝑥
  • E3𝑥

Q5:

List all factors of 𝑝𝑞.

  • A1,𝑝,𝑝,𝑝𝑞,𝑝𝑞,𝑞
  • B𝑝,𝑝,𝑝𝑞,𝑝𝑞,𝑞
  • C1,𝑝,𝑝,𝑝𝑞,𝑞
  • D1,𝑝,𝑝𝑞,𝑝𝑞,𝑞
  • E1,𝑝,𝑝,𝑝𝑞,𝑞

Q6:

Which of the following is a complete factorization of 65𝑥𝑦?

  • A5×𝑥×𝑦
  • B65×𝑥×𝑦
  • C5×13×𝑥×𝑦
  • D5×5×𝑥×𝑦
  • E13×𝑥×𝑦

Q7:

Which of the following is a complete factorization of 55𝑥𝑦?

  • A5×𝑥×𝑦
  • B55×𝑥×𝑦
  • C5×11×𝑥×𝑦
  • D5×5×𝑥×𝑦
  • E11×𝑥×𝑦

Q8:

Which of the following is a complete factorization of 51𝑥𝑦𝑧?

  • A3×𝑥×𝑦×𝑧
  • B51×𝑥×𝑦×𝑧
  • C3×17×𝑥×𝑦×𝑧
  • D3×3×𝑥×𝑦×𝑧
  • E17×𝑥×𝑦×𝑧

Q9:

Completely factor the following expression: 51𝑥.

  • A17⋅3⋅𝑥⋅𝑥
  • B17⋅3⋅𝑥⋅𝑥⋅𝑥
  • C51⋅𝑥⋅𝑥⋅𝑥
  • D51⋅𝑥
  • E17⋅3⋅𝑥

Q10:

Completely factor the following expression: 10𝑥.

  • A2⋅5⋅𝑥⋅𝑥⋅𝑥
  • B2⋅5⋅𝑥⋅𝑥
  • C10⋅𝑥⋅𝑥⋅𝑥
  • D10⋅𝑥
  • E2⋅5⋅𝑥

Q11:

Completely factor the following expression: 38𝑥.

  • A2⋅19⋅𝑥⋅𝑥⋅𝑥
  • B2⋅19⋅𝑥⋅𝑥
  • C38⋅𝑥⋅𝑥⋅𝑥
  • D38⋅𝑥
  • E2⋅19⋅𝑥

Q12:

Completely factor the following expression: 55𝑥𝑦.

  • A11⋅5⋅𝑥⋅𝑥⋅𝑦⋅𝑦
  • B11⋅5⋅𝑥⋅𝑥⋅𝑦
  • C55⋅𝑥⋅𝑦
  • D55⋅𝑥⋅𝑥⋅𝑦⋅𝑦
  • E11⋅5⋅𝑥⋅𝑦

Q13:

Completely factor the following monomial: 45𝑎𝑏𝑐.

  • A45×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐
  • B3×3×5×𝑎×𝑏×𝑏×𝑐×𝑐
  • C45×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐
  • D3×5×5×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐
  • E3×3×5×𝑎×𝑏×𝑏×𝑏×𝑐×𝑐

Q14:

Completely factor the following monomial: 15𝑎𝑏𝑐.

  • A3×5×𝑎×𝑏×𝑏×𝑏×𝑐×𝑐
  • B3×5×𝑎×𝑏×𝑏×𝑐×𝑐
  • C15×𝑎×𝑏×𝑏×𝑐×𝑐
  • D3×5×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐
  • E15×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐

Q15:

Completely factor the following monomial: 225𝑎𝑏𝑐.

  • A3×3×5×5×𝑎×𝑏×𝑏×𝑐×𝑐
  • B225×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐
  • C3×3×5×5×𝑎×𝑏×𝑏×𝑏×𝑐×𝑐
  • D3×5×5×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐
  • E225×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐

Q16:

List all factors of 6𝑎.

  • A1, 2, 3, 6, 𝑎, 2𝑎, 3𝑎, 6𝑎, 𝑎, 2𝑎, 3𝑎, and 6𝑎
  • B2, 3, 6, 𝑎, 2𝑎, 3𝑎, 6𝑎, 2𝑎, 3𝑎, and 6𝑎
  • C1, 2, 3, 𝑎, 2𝑎, 3𝑎, 𝑎, 2𝑎, and 3𝑎
  • D2, 3, 6, 𝑎, 2𝑎, 3𝑎, 6𝑎, 2𝑎, and 3𝑎
  • E1, 2, 3, 6, 2𝑎, 3𝑎, 6𝑎, 𝑎, 2𝑎, and 3𝑎

Q17:

Which of the following is a factored form of 24𝑥𝑦?

  • A2×3×𝑥×𝑦
  • B2×3×𝑥×𝑦
  • C2×3×𝑥×𝑦
  • D2×3×𝑥×𝑦
  • E2×3×𝑥×𝑦

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