Question

Find the least common multiple of x^2+x-12 and x^2+2x-15

a. (x+4)(x-3)(x+5)
b. (x-3)(x+5)(x-4)
c. (x+4)(x-3)(x-3)
d. (x+4)(x-5)(x-3)

Answer 1

First factorize the given quadratics as much as possible:

`x^2+x-12=(x+4)(x-3)`

`x^2+2x-15=(x+5)(x-3)`

Both share a common factor of
`x-3`. We have to multiply the first by
`x+5` and the second by
`x+4` in order to get a new expression that involves all the factors of both, so that the LCM is

`(x+4)(x+5)(x-3)`

making the answer A.