Remember that the dividing procedure for long division of integers finishes whenever the remainder is smaller than the divisor.
dividend equals divisor* quotient + remainder
Polynomial division follows a similar procedure. When the residue is smaller than the degree of the divisor, the division is completed.
According to the remainder theorem: If you divide a polynomial f(x) by a linear divisor (x – a), the remainder equals f (a). As a result, if the divisor is linear, the remainder may be calculated using the Remainder Theorem.
What is Remainder Theorem?
We already know a little about the remainder theorem, it is a method to Euclidean polynomial division. According to the Remainder theorem which we are going to discuss, dividing a polynomial P(x) by a factor (x – a); that isn’t an element of the polynomial yields a smaller polynomial and a remainder. This obtained residual is essentially a value of P(x) when x = a, more especially P (a).
x -a is therefore the divisor of P(x) if and only if P(a) = 0. The remainder theorem is known to be used to factor polynomials of any degree in an easy way.
Remainder Theorem – Definition
The Remainder Theorem starts with a polynomial, say p(x), where “p(x)” is a polynomial p with x as a variable. Then, according to the theory, divide that polynomial p(x) by some linear factor x – a, where an is just some number. A lengthy polynomial division is performed here, yielding some polynomial q(x) (the variable “q” stands for “the quotient polynomial”) and a polynomial remainder is r (x). It may be stated as follows:
p(x) divided by (x-a) equals q(x) + r(x)
How to Find Remainder of Polynomials?
How can the remainder and factor theorem be used to discover the remainder of polynomial divisions as well as the factors of polynomial divisions?
According to the Remainder Theorem, if a polynomial f(x) is divided by (x – k), the remainder r = f (k). It can aid in the factoring of more complicated polynomial expressions.
Now according to the Factor Theorem, which says that a polynomial f(x) has a factor (x – k) if and only if f(k) = 0. It is a variant of the Remainder Theorem in which the remainder equals zero.
Use of Remainder Theorem Formula
When a polynomial p(x) is divided by (ax + b), the remainder theorem formula is used to get the remainder. We may use the remainder theorem to determine whether (ax + b) is a factor of p(x). If the remainder is zero, (ax + b) is a factor of the polynomial p(x), else it is not. The remainder theorem formula’s principal use is the factor theorem. The remainder theorem is required to show the factor theorem.
Cuemath Classes
You’ve undoubtedly observed that the subject is simple to grasp. Problems requiring the Remainder Theorem will feel less difficult to solve if you have conceptual clarity on the subject, which is where Cuemath comes in. Cuemath is the most efficient online math services platform for establishing a solid mathematical foundation.
Cuemath is the world’s premier live online math education platform, ensuring that your mathematical foundation is solid. Cuemath classes offer students one-on-one connections with the greatest professors, allowing them to better understand math subjects. Teachers do a variety of additional activities, such as puzzle-solving, practical issue solving, and so on, to help pupils feel confident.
Visit the Cuemath website to understand more about these ideas in full. You may learn about the remainder theorem in an entertaining way by visiting this website!
Archives
- December 2023
- November 2023
- October 2023
- September 2023
- August 2023
- July 2023
- June 2023
- May 2023
- April 2023
- March 2023
- February 2023
- January 2023
- December 2022
- November 2022
- October 2022
- September 2022
- August 2022
- July 2022
- June 2022
- May 2022
- April 2022
- March 2022
- February 2022
- January 2022
- December 2021
- November 2021
- October 2021
- September 2021
- August 2021
- July 2021
- June 2021
- May 2021
- April 2021
- March 2021
- February 2021
- January 2021
- December 2020
- November 2020
- October 2020
- September 2020
- August 2020
- July 2020
- June 2020
- May 2020
- April 2020
- March 2020
- February 2020
- January 2020
- December 2019