Ads
related to: finding remainder when dividing polynomials examplesgenerationgenius.com has been visited by 10K+ users in the past month
- Grades 6-8 Math Lessons
Get instant access to hours of fun
standards-based 6-8 videos & more.
- K-8 Standards Alignment
Videos & lessons cover most
of the standards for every state
- Loved by Teachers
Check out some of the great
feedback from teachers & parents.
- K-8 Math Videos & Lessons
Used in 20,000 Schools
Loved by Students & Teachers
- Grades 6-8 Math Lessons
Search results
Results from the WOW.Com Content Network
The polynomial remainder theorem may be used to evaluate () by calculating the remainder, . Although polynomial long division is more difficult than evaluating the function itself, synthetic division is computationally easier. Thus, the function may be more "cheaply" evaluated using synthetic division and the polynomial remainder theorem.
Polynomial long division can be used to find the equation of the line that is tangent to the graph of the function defined by the polynomial P(x) at a particular point x = r. [3] If R ( x ) is the remainder of the division of P ( x ) by ( x – r ) 2 , then the equation of the tangent line at x = r to the graph of the function y = P ( x ) is y ...
The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed. [8] Polynomial division leads to a result known as the polynomial remainder theorem: If a polynomial f(x) is divided by x − k, the remainder is the constant r = f(k). [9] [10]
Finally, dividing r 0 (x) by r 1 (x) yields a zero remainder, indicating that r 1 (x) is the greatest common divisor polynomial of a(x) and b(x), consistent with their factorization. Many of the applications described above for integers carry over to polynomials. [ 139 ]
Ruffini's rule can be used when one needs the quotient of a polynomial P by a binomial of the form . (When one needs only the remainder, the polynomial remainder theorem provides a simpler method.) A typical example, where one needs the quotient, is the factorization of a polynomial p ( x ) {\displaystyle p(x)} for which one knows a root r :
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Its existence is based on the following theorem: Given two univariate polynomials a and b ≠ 0 defined over a field, there exist two polynomials q (the quotient) and r (the remainder) which satisfy = + and < (), where "deg(...)" denotes the degree and the degree of the zero polynomial is defined as being negative.
Ads
related to: finding remainder when dividing polynomials examplesgenerationgenius.com has been visited by 10K+ users in the past month