Table of Contents
Remainder Theorem:
The Remainder theorem is used to find the remainder of the long division of polynomials. The remainder of the division can be measured by the simple division. In the division of the polynomial, we use the terms Dividend, Quotient, Divisor, and Remainder. The simple formula for the Remainder theorem is as follows:
| Dividend = (Quotient * Divisor) + Remainder |
When you are using tools like the remainder theorem calculator by calculator-online.net, learn how to break down the whole procedure in small steps. This would make the question easy for the students to learn. We are trying to represent the easiest method to solve the Remainder of a question.
The Remainder and Division:
The Remainder theorem is the most common method used to solve long-division questions. Observe the long division question where you are able to find the divisor, dividend and quotient, and remainder. We are using such an example which makes the question easy for the students to learn when solving the Long Division questions. Students are actually not able to understand all the terms involved in the Division question, which makes the question more difficult for them. The polynomial 4x4 + 3x3 + 0x2 + 2x + 1 can be divided by the other polynomial like x2 + x + 2.
The polynomial remainder calculator makes the question easy for us and the remainder in this long division is 11x + 8.
We can write the polynomial as-
How to Factorize the Polynomials:
The factor theorem calculator can make it easy to factorize the polynomial like
| x2 + x – 6 = 0 The roots of the given polynomial are: x2 + x – 6 = 0 ⟹ x2 + 3x – 2x – 6 = 0 ⟹ x (x+3) – 2 (x+3) = 0 ⟹ (x+3) (x-2) = 0 ⟹ x + 3 = 0, x – 2 = 0 ⟹ x = -3, x = 2 |
The remainder factor theorem calculator precisely finds the factor of the polynomial, which are x = -3, x = 2.
Why Learn the Basic Concepts?
First, you need to learn about the terminologies, and then try to solve the long-division question for your convenience. When you are using the polynomial division calculator, it reveals what are the various steps in solving the long division method.
Once you have the basic concepts of the terminologies then it can become easy for you to understand the concept of the long division. The long division polynomials calculator is an online tool that verifies all the steps in detail for the students, and it makes the long division process fun to solve. If you are finding any difficulty in finding the remainder then the remainder calculator directly solves the long division questions.
Now consider the example of the Long division question, and observe how the divisor, the dividend, the quotient, and the remainder are generated in the long division question:
The remainder theorem calculator also finds the remainder of the polynomial of any power.
The Terms Used in Division:
Here 75 ÷ 4 = 18; R = 3, when using the long division method, it would be clear the Dividend here is 75, the Divisor is 4 and the remainder is 3, and the quotient here is 18. When you are a Polynomial Long Division Calculator, you can solve the long design of the polynomial, but it should be clear to you that the term divisor, dividend, Quotient, and the remainder should be clear to you.
| Dividend | The number which we are going to divide in the long division process | 75 |
| Divisor | The number which we are going to use to divide the dividend. | 4 |
| Quotient | It is the result of the long division | 18 |
| Remainder | The remaining number which can be divided | 3 |
Understanding one part of it is the quotient, the other part is the remainder, and one of it is the divisor. Technology is one of the most amazing things for making learning interactive.
Conclusion:
The remainder theorem makes the division easy, but it is essential to learn the different terms like the Quotient, Divisor, Remainder, and Dividend. The remainder theorem calculator makes the division of the polynomials easy. We can determine. It can be difficult to understand the long division if you aren’t able to understand the related terms.
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