First factorize the given quadratics as much as possible:
[tex]x^2+x-12=(x+4)(x-3)[/tex]
[tex]x^2+2x-15=(x+5)(x-3)[/tex]
Both share a common factor of [tex]x-3[/tex]. We have to multiply the first by [tex]x+5[/tex] and the second by [tex]x+4[/tex] in order to get a new expression that involves all the factors of both, so that the LCM is
[tex](x+4)(x+5)(x-3)[/tex]
making the answer A.
