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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