remainder theorem

Let us learn about remainder theorem

The Remainder Theorem is very useful for calculating, evaluating polynomials at a given value of x, though it might not seem so, at least at 1st blush. This is mainly because the tool is presented as a theorem with a proof & you probably don't feel ready for proofs at this stage in student’s studies. Fortunately, student doesn’t "have" to understand the proof of the Theorem; they just need to understand how to use the remainder theorem. If f(x) is a polynomial in x & it is divided by x-a; the remainder is the value of f(x) at x = a i.e., Remainder = f (a).

Proof of remainder theorem:

Let p(x) be a polynomial divided by (x-a).

Let q(x) is the quotient and R is the remainder.

By division algorithm, Dividend = (Divisor x quotient) + Remainder

P(x) = q(x). (x-a) + R

Substitute x = a,

P (a) = q (a) (a-a) + R

P (a) = R (a - a = 0, 0 - q (a) = 0)

Hence Remainder = p (a).

In our next blog we shall learn about associate connection I hope the above explanation was useful.Keep reading and leave your comments.