If a polynomial f(x) has a remainder of -9 when divided by x-3, what is f(3)?

Question

If a polynomial f(x) has a remainder of -9 when divided by x-3, what is f(3)?

Answer 1

I don't know if we need to know the order of the polynomial....let's try a possible solution:

 

consider (x-3)^2

expanded:  x^2 -6x + 9

add -9:

x^2 -6x 

for x = 3, value is -9 

coincidence?---try another option:

 

(x-3)(x+3) = x^2 - 9

add -9:

x^2 - 18

for x = 3, value is -9

 

One more:

(x-3)(2x+2) = 2x^2 - 4x - 6

add -9:

2x^2 -4x - 15

for x=3, 

2*9 -12 -15 = -9

 

It seems we have the answer, but how can we write a general equation?