SOLUTION: I am trying to study for a test and I can not figure how to do this question. The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3).

Question 78471: I am trying to study for a test and I can not figure how to do this question.
The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3).
a. -5
b. -2
c. 2
d. 3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We know that
"The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2"
So multiply both sides by to solve for f(x)

Now let y=x-3 to make multiplication easier

Distribute
Notice the y's cancel on the last term
Now replace y with x-3
Distribute

Combine like terms

So our function f(x) is . Notice if we divide f(x) by x-3 we get our original problem:

Now since we know the function is then f(3) is

So in other words, f(3)=2. So the answer is c)
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