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二项式定理 （英語： Binomial theorem）描述了 二项式 的 幂 的 代数 展开。 根据该定理，可以将两个数之和的整数次幂诸如 展开为类似 项之和的 恒等式，其中 、 均为非负整数且 。 系数 是依赖于 和 的正整数。 当某项的指数为0时，通常略去不写。 例如： [1] 中的系数 被称为 二项式系数，记作 或 （二者值相等）。 二项式定理可以推广到任意实数次幂，即 广义二项式定理[2]。 历史. 二项式系数的三角形排列通常被认为是法国数学家 布莱兹·帕斯卡 的贡献，他在17世纪描述了这一现象 [3]。 但早在他之前，就曾有数学家进行类似的研究。 例如，古希腊数学家 欧几里得 于公元前4世纪提到了指数为2的情况 [4][5]。 公元前三世纪，印度数学家 青目 探讨了更高阶的情况。
The remainder theorem states that when a polynomial p (x) is divided by a linear polynomial (x - a), then the remainder is equal to p (a). The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the long division.
Find the remainder when $7^{98} $ is divided by $5$. What I am doing here is expanding ${(5+2)}^{98} $ using binomial theorem and writing it as $5k + 2$, where $k$ is a positive integer but the an...
The Remainder Theorem. When we divide f (x) by the simple polynomial x−c we get: f (x) = (x−c) q (x) + r (x) x−c is degree 1, so r (x) must have degree 0, so it is just some constant r: f (x) = (x−c) q (x) + r. Now see what happens when we have x equal to c: f (c) = (c−c) q (c) + r. f (c) = (0) q (c) + r. f (c) = r. So we get this:
How to find the remainder in a binomial expression using the Binomial Theorem? Answer: Suppose you have to calculate the remainder of a number when divided by 17. Then, you must expand the...
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The remainder theorem allows us to quickly find the remainder of a polynomial when it is divided by a binomial. Division. A given polynomial can be decomposed into a quotient, divisor and remainder as follows: f (x) = q (x) (x-c) + r f (x) = q(x)(x−c)+ r. Where. f (x) f (x) is the polynomial, q (x) q(x) is the quotient, x-c x− c is the divisor and.
Theorem: Remainder Theorem Suppose \(p\) is a polynomial of degree at least \(1\) and \(c\) is a real number. When \(p(x)\) is divided by \(x − c\) the remainder is \(p(c)\).
