Question

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

Answer 1

Answer:

$5 {y}^{2} - 80$

Step-by-step 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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