Question

Find the least common multiple of the following polynomials: 5y^2-80 and y+4

a. (y+4)(y-4)
b. (y+4)
c. 5(y+10)(y-8)
d.5(y+4)(y-4)

Answer 1

`5y^2 - 80 = 5(y^2-16) = 5(y - 4)(y + 4)`

LCM of 5(y - 4)(y + 4) and (y + 4) is 5(y - 4)(y + 4)

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Answer: 5(y - 4)(y + 4) (Answer D)
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Answer 2

Answer: The correct option is (d)
`5(y+4)(y-4).`

Step-by-step explanation: We are given to find the least common multiple of the following polynomials:

`P_1=5y^2-80,\\\\P_2=y+4.`

The LEAST COMMON MULTIPLE of two or more polynomials is a polynomial of the least degree that is divisible by all the other polynomials.

We have

`P_1=5y^2-80=5(y^2-16)=5(y^2-4^2)=5(y+4)(y-4).`

Therefore, the least common multiple of the polynomials will be

`LCM(P_1,P_2)=5(y+1)(y-1).`

Thus, (d) is the correct option.