Question

Find the least common multiple (LCM) of the polynomials y2 – 16 and 5y + 20.

Answer 1

The polynomial is given as,

`y^2\text{ - 16 and 5y + 20}`

Simplifying the first expression,

`\begin{gathered} y^2-16=y^2-4^2 \\ y^2-16=\text{ ( y - 4 )( y + 4 )} \end{gathered}`

Simplifying the second expression,

`5y\text{ + 20 = 5( y + 4)}`

The common factor is given as,

`\text{Common factor = ( y + 4 ) }`

Uncommon factors are given as,

`\text{Uncommon factor = ( y - 4 ) }*\text{ 5}`

LCM is calculated as,

`\text{LCM = 5}*(\text{ y - 4 )( y + 4 )}`

Thus the LCM of the given expression is,

`\text{ 5}*(\text{ y - 4 )( y + 4 )}`