大家容易想到的是long division: 于是得到remainder就是4。 通过上面的例子可以知道一个polynomial ÷ (x-c)的remainder也是一个value,重点是这样一个value如何快速高效的求出来??记住,快速高效!! 神奇且实用的Remainder theorem就可以高效地,记住...
Polynomial 是多项式。稍微证明一下这个 theorem. 目前还没看懂这个 theorem 在说什么、也不想看证明的,直接跳过去,先看题。 所以,问polynomialf(x)除以(x-a)的余数 (remainder), 就是f(a); 反过来,题目给了f(a), 就是 polynomialf(x) 除以(x-a) 的...
可以看到长除法很麻烦,计算量比较大、容易做错,那么下面介绍一个Remainder Theorem来快速解决: 如果要算一个多项式p(x)除以(x−c)的余数,那么只需要把x=c带入到p(x)中,即p(c)就是所求余数。针对上述例题,p(3)=2×33−7×32+5=−4。 下面给出证明: 一个多项式p(x)除以d(x)一定能表示成: p(...
The remainder theorem states that if a polynomial f(x) is divided by a linear function x - k the remainder is f(k). Proof: In any division dividend = divisor X quotient + remainder Let Q(x) be the quotient and R be remainder. f(x) = (x - k) Q(x) + R f(k) ...
How To: Given a polynomial functionff, evaluatef(x)f(x)atx=kx=kusing the Remainder Theorem. Use synthetic division to divide the polynomial byx−kx−k. The remainder is the valuef(k)f(k). Example 1: Using the Remainder Theorem to Evaluate a Polynomial ...
Remainder theorem: If a polynomial P(x) of degree n ≥ 1 is divided by x - b, where b is a constant, then the remainder is P(b).A couple of examples illustrating the remainder theorem Example #1 In the lesson about polynomial long division, we ended with the following result:...
(多项式)因式分解定理(Factor theorem)与多项式剩余定理(Polynomial remainder theorem)(多项式长除法),程序员大本营,技术文章内容聚合第一站。
(多项式的)因式分解定理(factor theorem)是多项式剩余定理的特殊情况,也就是余项为 0 的情形。 0. 多项式长除法(Polynomial long division) Polynomial long division - Wikipedia 1. 因式分解定理 Factor theorem 该定理表达的是,多项式f(x)存在因子x−k当且仅当f(k)=0(余数为 0,也即k是其根)。
Remainder Theorem If a polynomialP(x) is divided by (x–r), then the remainder of this division is the same as evaluatingP(r), and evaluatingP(r) for some polynomialP(x) is the same as finding the remainder ofP(x) divided by (x–r)....
Understand the remainder theorem and how to use the remainder theorem. Read the definition of the factor theorem and learn its formula.