Question 72090
<pre>
When a polynomial f(x) is divided by x - a , the remainder is f(a).

Remember basic arithmetic:  Dividend = Divisor  x Quotient + Remainder.

The polynomial f(x) divided x-3 results in a quotient of x2 + 3x -5 with a remainder of 2. Find f(3). 

obviously, the reminder will be 2. 

Proof:
Let say you have f(x)= x^3 - 14x + 17 and is divided by x - 3

Let's divide using long division:
                     x^2 + 3x -5
                _________________
          x -3  |x^3     -14x + 17
                 <u>x^3-3x^2</u>
                     3x^2-14x
                     <u>3x^2-9x</u>
                         -5x + 17
                         <u>-5x + 15</u>
                                2 --------->Reminder

 Using f(x)= x^3 - 14 + 17, we are going to find the reminder p(x) = x-3

 f(a) = reminder
 f(3) = x^3 - 14x + 17
      = 3^3 - 14(3) + 17
      = 27 - 42 + 17
      = 44 - 42
      = 2
f(3) = 2 therefore, the reminder is 2