How do you find the least commmon multiple of x2 -4x-5 and x2-3x-10?

Answer 1

First, try to factor both expressions:

x2 - 4x - 5

= (x - 5)(x + 1)

x2 - 3x - 10

= (x - 5)(x + 2)

So both expressions have (x - 5) as a factor, which means you only need to include that once between the two of them. The least common multiple then would be:

(x - 5)(x + 1)(x - 2)

If you need to expand that out, it becomes:

(x - 5)(x2 - x - 2)

= x3 - x2 - 2x - 5x2 + 5x + 10

= x3 - 6x2 + 3x + 10