Understanding the Remainder Theorem to Solve Polynomial Division Problems

In algebra, the remainder theorem is one of the keys used to find solutions to many polynomial division problems.

If you are feeling it difficult to apply this mathematical technique, just stop worrying and use the advanced remainder calculator Calculatored. This online tool is specifically designed to give you an accurate solution for polynomial division remainder.

In the following post below, we will explore the best tools that could assist you to calculate the remainder in algebraic problems. Also, we will focus on how you could carry out complicated calculations by hand.

Remainder Theorem Calculation 

In the following section, we will be discussing the manual method for the calculations of the remainder theorem. Let’s get to it!

Remainder Theorem Statement

In algebra, the remainder theorem is defined as

“A number that yields after dividing a polynomial by a certain linear factor”

Remainder Theorem Proof

Let’s make a supposition that when we divide a polynomial p(x) by a linear factor (x-a), the resulting remainder and quotient are q(x) and r, respectively. Now here, this remainder can instantly be determined by using the remainder calculator.

As we know the basic division algorithm is

Dividend = (Divisor × Quotient) + Remainder

And using the equation p(x) = (x – a) · q(x) + r, we have to put the value of x in the original polynomial

p(a) = (a – a) *q(a) + r

p(a) = (0) * q(a) + r

p(a) = r

Which is the final remainder that could instantly be figured out by using the remainder calculator.

Various definitions and terminology:

There are various terms that are essential to remember:

Dividend:

It is the quantity which is divided by a number. For example the term 45/5, 9/3,14/2, etc. The terms 45, 9, and 14 are the dividends in the fractions, it means it is the numerator of the fraction.

Divisors:

The terms which are used to divide a dividend are called the divisor of the division process. In terms 45/5, 9/3,14/2, etc, the denominators 5,3, and 2 are the divisors.

Quotient:

The quotient is the quantities multiplied by the divisors to find the answer. You can say the 45/5, 9/3,14/2, etc. The 9, 3, and 7 are the quotients of the division process.

Remainders: 

The remainder is the remaining amount of the division and these are quantities gathered after the subtraction. In the given example the “3” is the remainder of the division.

Things To Remember!

While applying the remainder theorem, make sure that

The Divisor factor is linear

You can never find a quotient with a remainder theorem
The basic formula remains the same for always

Conclusion

The remainder theorem is used to find the answer to the various algebraic terms. But it is quite essential to understand all the basic terms of the division process like the dividend, divisor, quotient, and the remainder. These terms are used in the remainder theorem to find the answers.