Answer:
A) [tex]12y^{3}[/tex]
Step-by-step explanation:
A) [tex]\frac{12y^{3} }{6y^{2} }[/tex]
[tex]=\frac{2y(6y^{2} )}{6y^{2}}[/tex]
= 2y
B) [tex]\frac{24y}{6y^{2} }[/tex]
[tex]=\frac{4}{y}[/tex]
Hence, [tex]12y^{3}[/tex] is divisible by [tex]6y^{2}[/tex] and the correct option is (A).
Option: A is the correct answer.
A) 12y³
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.
