Question

Which monomials are divisible by 6y^2?

Choose all apply:
A)12y^3
B)24y
C)None of the above

Answer 1

Option: A is the correct answer.

A) 12y³

Explanation:

We are asked to find the monomials which are divisible by 6y².

We know that a monomial is divisible by the other monomial if it contain all the factor of the divisor monomial.

The factors of the divisor monomial are:

6y²=2×3×y×y

A)

12y³

The factor of this dividend monomial is:

12y³=2×2×3×y×y×y

The monomial contains all the factors of the divisior monomial.

Hence, it is divisible by 6y².

B)

24y

The factor of this dividend monomial is:

24y=2×2×2×3×y

The monomial does not contains all the factors of the divisior monomial.

Hence, it is not divisible by 6y².

Answer 2

A)
`12y^(3)`

Explanation:

A)
`(12y^(3) )/(6y^(2) )`

`=(2y(6y^(2) ))/(6y^(2))`

= 2y

B)
`(24y)/(6y^(2) )`

`=(4)/(y)`

Hence,
`12y^(3)` is divisible by
`6y^(2)` and the correct option is (A).