When a polynomial P (x) is divided by x +3, the remainder is 2. Which point must be on the
graph of the corresponding function y = P (x)?

Question

When a polynomial P (x) is divided by x +3, the remainder is 2. Which point must be on the 
graph of the corresponding function y = P (x)?

anonymous · Answer

A. −3, −2 
 B.  −3, 0 
 C.  −3, 2 
 D. 3, 2

anonymous · Answer

I tried reverse engineering the question to get me x+5 for P(x) but that doesn't work for any of the points.

anonymous · Answer

$$\frac{P(x)}{x+3}=Q(x)+\frac{2}{x+3}$$
Because there's a remainder when you divide, you know that $(x+3)$ is not a factor of $P(x)$, and so $x=-3$ is not a root. This means you can eliminate (b) $(-3,0)$.

From the Remainder Theorem we also have
$$P(x)=(x+3)Q(x)+2$$
Plugging in $x=-3$, we have
$$P(-3)=(-3+3)Q(-3)+2=2$$
which is the point $(-3,2)$.