If x=a is a zero of f(x) then (x-a) is a factor of f(x). Then, since x= 4,6,-7 are all zeros of f(x), we may
write f(x) = (x-4)(x-6)(x+7) = (x-4)(x^2 + x - 42) = x^3 -3x^3 -46x +168. This is choice B. I have no
difficulty in expanding and mentally collecting terms to write the coefficients of descending powers of x in 1 step as I proceed. This is a very useful technique. It forces a systematic, concentrated method on one which prevents sloppy mistakes.