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
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
What is the prime factorization of the following monomials?
a) 28 xy 2
b) 32 x 3y
c) 70 x 3y 3
d) 120 x 2y 2
Find the prime factorizations of 5 xy 2 and 20 x 3y and then the prime factorization of 100 x 4y 3 knowing that 100 x 4y 3 = (5 xy 2) × (20 x 3y)
Solutions to the Above Questions
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.
Solution
a) 28 xy 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
Solution
The prime factorization of 5 xy 2 is.
5 xy 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 xy 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