Which is NOT a common factor of the following monomials?
16xy^2y, 12xy, 8xy^2
a) 4x
b) 4y
c) xy
d) x^2y^2
I think the answer is d
there is no x^2 in all of them so d is correct
Thank you
To determine which is NOT a common factor of the given monomials, we need to find the factors of each monomial and then identify the factor that is not common to all three.
Let's find the factors of each monomial:
1. 16xy^2:
Factors: 1, 2, 4, 8, 16, x, y, y
Notice that the factors of 16xy^2 are: 1, 2, 4, 8, 16, x, y, y.
2. 12xy:
Factors: 1, 2, 3, 4, 6, 12, x, y
Notice that the factors of 12xy are: 1, 2, 3, 4, 6, 12, x, y.
3. 8xy^2:
Factors: 1, 2, 4, 8, x, y, y
Notice that the factors of 8xy^2 are: 1, 2, 4, 8, x, y, y.
Now, let's check which factor is not common to all three monomials:
a) 4x: This factor is common to all three monomials.
b) 4y: This factor is common to all three monomials.
c) xy: This factor is common to all three monomials.
d) x^2y^2: This factor is NOT common to all three monomials. It is only a factor of the monomial 16xy^2.
Therefore, the correct answer is d) x^2y^2.
To determine which factor is NOT common among the given monomials, we need to find the factors that are present in all the monomials and identify the factor that does not appear in any of them.
Let's analyze the given monomials individually:
1) 16xy^2y: The factors in this monomial are 2, 2, 2, x, y, and y.
2) 12xy: The factors in this monomial are 2, 2, 3, x, and y.
3) 8xy^2: The factors in this monomial are 2, 2, 2, x, y, and y.
To find the common factors, we look for factors that are present in all three monomials:
Common factors:
- 2 (appears in all monomials)
- x (appears in all monomials)
- y (appears in all monomials)
Now, let's examine the answer choices:
a) 4x: This choice contains the factor x, which is common among all the monomials.
b) 4y: This choice contains the factor y, which is common among all the monomials.
c) xy: This choice contains both factors x and y, which are common among all the monomials.
d) x^2y^2: This choice contains the factors x and y squared, but neither of these factors appear in the monomials.
Therefore, the correct answer is d) x^2y^2 because it is the factor that does not appear in any of the given monomials.