In the “Proving Grounds” Quiz 1 #5, this question is given:

p(x) = ax^2 + bx + c

q(x) = ax^2 + bx + d

The functions p(x) and q(x) are defined above, and a, b, c, and d are constants. If x – 3 is a factor of p(x) and d is 8 greater than c, what is the remainder when q(x) is divided by x – 3?

In your answer explanation, you state:

“…We know that, as a general rule, the remainder when a polynomial f(x) is divided by x – a is f(a).”

Can you explain this further?