In cases where we don’t know the function, but we are given the remainder and divisor, but no quotient or function, we can leverage the division statement to help us.
Question
When x+2 is divided into f(x), the remainder is 3. determine the remainder when x+2 divided into f(x)+1?
Solution
The division statement for the first case is:
f(x) = (q(x))(x+2) + 3
then, the second case is
f(x) + 1 = (q(x))(x+2) + 3 + 1
f(x) + 1 = (q(x))(x+2) + 4
Very simple.