Remainder Theorem

About Remainder Theorem

When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. The remaining is the number of items left over after a particular number of items are sorted into groups with an equal number of items in each group. After division, it is something that "remains." Let's have a look at the remainder theorem.

What Is the Remainder Theorem?

The remaining theorem goes like this: The remainder is obtained by r = a when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k. (k). The remainder theorem allows us to calculate the remainder of any polynomial divided by a linear polynomial without actually performing the division algorithm steps.

Remainder Theorem Formula

p(x) = (x-c)q(x) + r is the generic formula for the remainder theorem (x). To show the remainder theorem formula, we'll use polynomials.

When p(x) is divided by (x-a)

Remainder = p(a)

OR

When p(x) is divided by (ax+b)

Remainder = Remainder Theorem

Proof for the Remainder Theorem

Dividend = (Divisor × Quotient) + Remainder.

r(x) is constant then, p(x) = (x-c)·q(x) + r.

Let’s put x=c

p(c) = (c-c)·q(c) + r

p(c) = (0)·q(c) + r

p(c) = r

Hence, proved.

Important Notes about Remainder Theorem

The remainder is obtained by r = a when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k. (k)

  • p(x) = (x-c)q(x) + r(x). is the remainder theorem formula
  • Dividend = (Divisor × Quotient) + Remainder.

Download free pdf of  Remainder Theorem Its Use And Solved Examples

Remainder Theorem
Remainder Theorem

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