Prime Factorization of Monomials - Questions With Solutions

# Prime Factorization of Monomials - Questions With 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