Question

Find the least common multiple of the following polynomials: 5y2 -80 and y + 4.

Answer 1

`5 {y}^(2) - 80`

Explanation:

The given polynomials are:

`5 {y}^(2) - 80`

and

`y + 4`

Let us factor the first polynomial to get:

`5 {y}^(2) - 80 = 5( {y}^(2) - 16)`

We need to rewrite as difference of two squares:

`5 {y}^(2) - 80 = 5( {y}^(2) - {4}^(2) )`

We can now factor to get:

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

So the least common multiple of

`5( {y} + 4)(y - 4) \: and \: (y + 4) \: is \: 5( {y} + 4)(y - 4) = 5 {y}^(2) - 16`

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