Worksheet: Prime Factorization of Monomials

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.

  • A133𝑥𝑥𝑦𝑦
  • B133𝑥𝑥𝑦
  • C39𝑥𝑦
  • D39𝑥𝑥𝑦𝑦
  • E133𝑥𝑦

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.

  • A173𝑥𝑥
  • B173𝑥𝑥𝑥
  • C51𝑥𝑥𝑥
  • D51𝑥
  • E173𝑥

Q10:

Completely factor the following expression: 10𝑥.

  • A25𝑥𝑥𝑥
  • B25𝑥𝑥
  • C10𝑥𝑥𝑥
  • D10𝑥
  • E25𝑥

Q11:

Completely factor the following expression: 38𝑥.

  • A219𝑥𝑥𝑥
  • B219𝑥𝑥
  • C38𝑥𝑥𝑥
  • D38𝑥
  • E219𝑥

Q12:

Completely factor the following expression: 55𝑥𝑦.

  • A115𝑥𝑥𝑦𝑦
  • B115𝑥𝑥𝑦
  • C55𝑥𝑦
  • D55𝑥𝑥𝑦𝑦
  • E115𝑥𝑦

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.