Answer:
The Least Common Multiple of polynomials is
[tex]5(y+4)(y-4)[/tex]
Step-by-step explanation:
Given : Polynomials [tex]5y^2-80[/tex] and [tex]y+4[/tex]
To find : LCM of the given polynomials
Solution :
First we find the factors of the polynomial [tex]5y^2-80[/tex]
[tex]5y^2-80=5(y^2-16)[/tex]
[tex]5y^2-80=5(y^2-4^2)[/tex]
Apply [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]5y^2-80=5(y+4)(y-4)[/tex]
The LCM of some numbers is the smallest number that the numbers are factors of.
The LCM of 5 is result of multiplying all prime factors, the greatest number of times they occur in either number.
So, LCM of 5 is 5
The LCM of (y+4)(y-4),(y+4) is the result of multiplying all factors, the greatest number of times they occur in either term.
So, LCM of (y+4)(y-4),(y+4) is (y+4)(y-4)
Therefore, The Least Common Multiple of polynomials is [tex]5(y+4)(y-4)[/tex]
