Question 388133
Using the rational root theorem, the possible rational roots are -3, -1, 1, or 3.  Now m(-1) = 2, m(1) = 12, m(3) = 78, but m(-3) = 0, so x = -3 is a (rational) root.  By performing synthetic division, the quotient after dividing {{{m(x)= x^3+4x^2+4x+3}}} by x + 3 is {{{x^2 + x + 1}}}, but the roots of this are complex, therefore -3 is the only rational root.