What is the remainder of

(x3 - 6x - 9x + 3) : (x - 3)

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.

remainder is f (3)

3^3 - 6*3^2 - 9*3 + 3

= 27 - 54 - 27 + 3

= - 51