Remainder of polynomial division

Thread starter songoku
Start date Oct 10, 2020
Tags

Division Polynomial Polynomial division Remainder

In summary, the remainder of polynomial division refers to the number or expression left over when one polynomial is divided by another. It is important because it helps us fully describe the relationship between two polynomials and can also aid in determining whether a polynomial is a factor of another. The calculation of the remainder of polynomial division involves using the polynomial long division method. It can be negative, but is usually positive. The remainder can also be used to solve equations by identifying factors and checking solutions.

Oct 10, 2020

songoku

Homework Statement: Find the remainder when ##x^{2017} + 1## is divided by ##(x-1)^2##

Relevant Equations: Remainder Theorem

##x^{2017} + 1 = Q(x) . (x-1)^2 + ax + b## where ##Q(x)## is the quotient and ##ax+b## is the remainder

##x=1 \rightarrow 2 =a+b##

Then how to proceed?

Thanks

Physics news on Phys.org

Oct 10, 2020

PeroK

Science Advisor

Homework Helper

Insights Author

Gold Member

2023 Award

If in doubt differentiate.

Oct 10, 2020

songoku

Thank you very much PeroK

1. What is the remainder of polynomial division?

The remainder of polynomial division is the value left over after dividing one polynomial by another. It is the part of the dividend that is not evenly divisible by the divisor.

2. How is the remainder of polynomial division calculated?

The remainder of polynomial division is calculated by dividing the dividend by the divisor and then subtracting the product of the quotient and divisor from the dividend.

3. What is the significance of the remainder in polynomial division?

The remainder in polynomial division is significant because it represents the error or difference between the dividend and the closest multiple of the divisor. It can also be used to determine if the division was successful or not.

4. Can the remainder of polynomial division be negative?

Yes, the remainder of polynomial division can be negative. This can occur when the dividend is smaller than the divisor, resulting in a negative value for the remainder.

5. How is the remainder of polynomial division used in real-world applications?

The remainder of polynomial division is used in various fields such as engineering, physics, and computer science. It is used for error correction in data transmission, finding roots of equations, and in polynomial interpolation for data analysis.