 # 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