SOLUTION: The polynomial f(x) divided x-3 results in a quotient of x2 + 3x -5 with a remainder of 2. Find f(3). possible answers: -5 -2 2 3 Please show me how to do this, so I can

Question 72090: The polynomial f(x) divided x-3 results in a quotient of x2 + 3x -5 with a remainder of 2. Find f(3).
possible answers:
-5
-2
2
3
Please show me how to do this, so I can have an example to go by.
Thanks to everyone who has given me examples to study in the past week. I took a practice test and with your examples, I did very well,
Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!



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

                 x^3-3x^2

                     3x^2-14x

                     3x^2-9x

                         -5x + 17

                         -5x + 15

                                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 

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