As per the statement of the remainder theorem:
Let $P(x)$ be any polynomial of degree greater than or equal to $1$ and "$a$" be any real number. If $P(x)$ is divided by $(x-a)$, then the remainder is equal to $P(a)$.
In the statement of the remainder theorem, why is it necessary that the degree of $P(x)$ is greater than or equal to one? If the degree of the polynomial is less than $1$ i.e. "$0$" then we will have a constant polynomial and when we divide it by a linear polynomial $(x-a)$, where "$a$" is a real number, then also the remainder is $P(a)$. For example , lets say $P(x) = 2x^0$. Then if we divide $P(x)$ by $(x-a)$, by following long division method we get quotient as "$0$" and remainder as $2 = 2x^0 = 2a^0 = P(a)$. Please clarify this for me.
Best Answer
It isn't necessary that $P(x)$ have degree greater than $1$. However, I think that if $P(x)$ has a degree of $0$, the result is very trivial.