# What is Remainder Theorem?

A remainder theorem is an approach of Euclidean division of polynomials.

## Answer: The remainder theorem states that if you divide any given polynomial f(x) by (x – h), then the resulting remainder is f(h).

The Remainder Theorem is useful for evaluating polynomials at a given value of x.

**Explanation:**

The remainder theorem is stated as follows: When a polynomial f(x) is divided by a linear polynomial (x-h), then according to the theorem, remainder equals f(h). Thus, we can skip the long division method, and can easily calculate the remainder of the polynomial by evaluating the given polynomial for x = h

The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the division algorithm.

The general formula for remainder theorem when f(x) is divided by (x-h) is, f(x) = (x-h) × q(x) + f(h)

### Thus, as per the remainder theorem, if you divide any given polynomial f(x) by (x – h), then the resulting remainder is f(h).

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