Polynomial Remainder Theorem. That is, if you have a function , and you divide it with another function , then the remainder of the division is equals to . Proof:
Let's say you have a function , where is the quotient (the result of dividing with ) and is the remainder (after dividing with ). According to the Polynomial Division Algorithm, the remainder of the division must have a smaller degree than the divisor, in this case, . Since has a degree of 1, must be a constant polynomial.
Now, if you substitute into the function, you'll end up with:
Therefore, the remainder is equals to .