# 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.

 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. 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 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