Prime Factorization of Monomials - Questions With Detailed Solutions

What is prime factorization of monomials? Grade 11 examples and questions are presented along with Solutions and explanations included.

Review of Monomials and Prime Factorization

A monomial is the product of a real number and variables raised to non negative integer powers.
Example of monomials: 2 x , -5 x 2y , 30 x 2y 4
What is prime factorization of monomials?
The prime factorization of a monomials is obtained by writing the whole number in the monomial in prime factorization followed by the product of the variables.
Examples of monomials in prime factorization form
1) 10 x = 2 5 x
2) 20 x 2 = 2 2 5 x x
3) - 30 x 2y 3 = - 2 3 5 x x y y y

Questions

  1. Which of the following is not a prime factorization?
    a)2 10 x
    b) 2 7 x x
    c) 4 4 4 x x y y y
    d) 2 2 2 3 x x y y
  2. What is the prime factorization of the following monomials?
    a) 28 x y 2
    b) 32 x 3y
    c) 70 x 3y 3
    d) 120 x 2y 2
  3. Find the prime factorizations of 5 x y 2 and 20 x 3y and then the prime factorization of 100 x 4y 3 knowing that 100 x 4y 3 = (5 x y 2) (20 x 3y)

Solutions to the Above Questions

  1. Solution
    a) The 10 in 2 10 x is not a prime number and therefore 2 10 x is not a prime factorization.
    b) 2 7 x x is a prime factorization.
    c) The 4 in 4 4 4 x x y is not a prime number and therefore 4 4 4 x x y is not a prime factorization.
    d) 2 2 2 3 x x y y is a prime factorization.

  2. Solution
    a) 28 x y 2 = 2 2 7 x y y
    b) 32 x 3y = 2 2 2 2 2 x x x y
    c) 70 x 3y 3 = 2 5 7 x x x y y y
    d) 120 x 2y 2 = 2 2 2 3 5 x x y

  3. Solution
    The prime factorization of 5 x y 2 is.
    5 x y 2 = 5 x y y
    The prime factorization of 20 x 3y is.
    20 x 3y = 2 2 5 x x x y
    The prime factorization of 100 x 4y 3 is.
    100 x 4y 3 = (5 x y 2) (20 x 3y) =
    (5 x y y ) (2 2 5 x x x y ) =
    2 2 5 5 x x x x y y y

More References and Links

Prime Factorization
Prime Factors
High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
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