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 ^{ 3}y
c) 70 x ^{ 3}y ^{ 3}
d) 120 x ^{ 2}y ^{ 2}
Solution
a) 28 x y^{ 2} = 2 × 2 × 7 × x × y × y
b) 32 x ^{ 3}y = 2 × 2 × 2 × 2 × 2 × x × x × x × y
c) 70 x ^{ 3}y ^{ 3} = 2 ×5 × 7 × x × x × x × y × y × y
d) 120 x ^{ 2}y ^{ 2} = 2 × 2 × 2 × 3 × 5 × x× x × y

Find the prime factorizations of 5 x y^{ 2} and 20 x^{ 3}y and then the prime factorization of 100 x^{ 4}y^{ 3} knowing that 100 x^{ 4}y^{ 3} = (5 x y^{ 2}) × (20 x^{ 3}y)
Solution
The prime factorization of 5 x y^{ 2} is.
5 x y^{ 2} = 5 × x × y × y
The prime factorization of 20 x^{ 3}y is.
20 x^{ 3}y = 2 × 2 × 5 × x × x × x × y
The prime factorization of 100 x^{ 4}y^{ 3} is.
100 x^{ 4}y^{ 3} = (5 x y^{ 2}) × (20 x^{ 3}y) =
(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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