The remainder theorem says [tex]x-c[/tex] is a factor of a polynomial [tex]p(x)[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]x^3+7x^2+4x-12[/tex] when [tex]x=-6[/tex]. We have
[tex](-6)^3+7(-6)^2+4(-6)-12=0[/tex]
so [tex]x+6[/tex] is indeed a factor.
