Solutions to Questions on Prime Factorization of Monomials

Solutions to prime factorization of monomials questions ? Grade 11 math questions are presented along with detailed solutions. Detailed Solutions and explanations are included.

  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
    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. 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
    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. 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)
    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

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