From the given real roots (and their multiplicities) we can construct a polynomial in factored form with a leading coefficient, a, which we can then solve for using the given point as follows:
f(x) = a(x + 2)(2x - 1)2
f(-3) = a (-1)(-7)2 = 5
a = - 5/49
f(x) = - 5/49(x + 2)(2x - 1)2