What is the LCM of x^2+5 and x^2+10x+25?

(x+5) ² (x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x (x+5) + 5 (x+5

= (x+5) (x+5)

= (x+5) ²

The LCM can be calculated as thus

| x²+5, (x+5) ²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 * x+5 * x²+5

The LCM will be the product of the three functions i. e

(x+5) ² (x²+5)

This hives the required expression.