Question

What is the remainder of (x3 – 6x – 9x + 3) ÷ (x - 3)

Answer 1

 remainder is f(3) 
3^3 - 6*3^2 - 9*3 + 3 
= 27 - 54 - 27 + 3 
= -51

Answer 2

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.