Question

plz friends.. explain me about the remainder theorem

Answer 1

In this you put the given value of x in the expression
The no. left will be the remainder of that equation.
But there is a difference between remainder and factor theorem. In remainder theorem the remainder can be any no. but in factor theorem the remainder should be 0.

Answer 2

Consider the polynomial g(x) of any degree greater than or equal to one and any real number c. If g(x) is divided by a linear polynomial (x-c), then the remainder is equal to g(c).

That is,

g (x) = (x - c) q(x) + g(c).

Proof of the Remainder theorem:

Consider the polynomial g(x) is divided by (x - c).

Let q(x) be the quotient and R be the remainder. Then, by using the division algorithm,

Thus, g(c) = R.

Hence, the remainder is g(c).