To do this easily, we will use the Factor and Remainder Theorem. When a polynomial is divided by a binomial, equate the binomial to zero to get the value of x. Then, substitute this x to the polynomial. Whatever the answer is, is the remainder.
x - 3 = 0
x = 3
x^3 - 6x - 9x +3
x^3 -6(3) - 9(3) + 3 = -15
Take its absolute value. The remainder would be 15.
