According to the factor theorem, if is a polynomial and for some number then is divisible by

This follows easily from the remainder theorem, because for the remainder is So if the remainder is 0 and is divisible by

The factor theorem can be used to obtain factors of a polynomial.

For example, if , then it is easy to check that So by the factor theorem is a factor of

According to the remainder theorem, if a polynomial is divided by where is any real number, the remainder is That is, , for some polynomial