Common
Polynomial remainder theorem
On the remainder of division by x – r
Polynomial remainder theorem
In algebra, the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states that, for every number r {\displaystyle r} , any polynomial f ( x ) {\displaystyle f(x)} is the sum of f ( r ) {\displaystyle f(r)} and the product of x − r {\displaystyle x-r} and a polynomial in x {\displaystyle x} of a degree one less than the degree of f {\displaystyle f} . In particular, f ( r ) {\displaystyle f(r)} is the remainder of the Euclidean division of f ( x )...
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