Thread: Functions

If you have

I know f(x) just means the function of x, or just y.

But take this:

If

then

Where r= remainder
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?

Edit: normally f(x),f(c),f(g) are all put in the place of possible functions, but this one is not.

Originally Posted by integral

If

then

Where r= remainder
This makes no since to me. some function divided by x-k yields the function of k.

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:

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 .