The method I used to get the answer is the same 'long division' procedure used by xarqi in his answer to your previous question,
I recommend this method.
First, arrange the polynomial that you are dividing v-4 into (the dividend), in order of terms of decreasing power, which in this case is
v^3 - 6 v^2 +9v -4 .
To get an v^3 term in the dividend, you need a v^2 in the quotient, etc. Fortunately the remainder is zero at the end of the process, otherwise the dividend polymomial could not be factored into polynomials of lower order.