If you have
I know f(x) just means the function of x, or just y.
But take this:
Where r= remainder
(Headbang) This makes no since to me. some function divided by x-k yields the function of k.
How do you come up with a function? (Crying)
Edit: normally f(x),f(c),f(g) are all put in the place of possible functions, but this one is not.
This statement is deduced based on the 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:
Originally Posted by integral
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 .