Question

Find the LCD for 5/2n^2+21n+27, 8n/2n^2-n-6.

Answer 1

`(5)/((2n+3)(n+9)),(8)/((2n+3)(n-2))`

1) Examining the Polynomial

`\begin{gathered} (5)/(2n^2+21n+27) \\ (5)/((2n^2+21n)+27) \\ (5)/(n(2n+21)+27) \\ (5)/((2n+3)(n+9)) \end{gathered}`

Let's find the Least Common Divisor, we need to factor the polynomial, then look for what we get.

In this case, factoring the denominator we have that as the LCM since (2n+3)(n+9) is the simplest form.

b) Writing the equation and factoring we can have:

`\begin{gathered} (8n)/(2n^2-n-6) \\ (8n)/((2n^2-n)-6) \\ (8n)/(n(2n-1)-6) \\ \\ (8)/((2n+3)(n-2)) \end{gathered}`

So, in short, to find the LCM of a polynomial is simply factorizing a polynomial to its simplest form.