polynomials

简明释义

英[/pəˈnɪəʊmɪəl/]美[/pəˈnɑːmiəl/]

n. [数]多项式（polynomial 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.The resultant is an important concept over the theory of polynomials.

结式是多项式理论中的一个重要概念。

2.A class of relaxation hybrid algorithm is defined to add varying relaxation factors into the iteration polynomials.

本文通过在迭代多项式中加入变化的松弛因子定义了一类松弛混合算法。

3.Use the information of the matching roots, and the character of the degree sequence and matching polynomials to compute.

利用匹配多项式根的信息，根据其定义以及图的度序列和匹配多项式的性质推导。

4.D dissertation is concerned with the dynamics of biquadratic polynomials.

本文主要研究双二次多项式的动力系统。

5.Thus we gave a kind of new method for solving the greatest common factor of two-variable polynomials.

利用矩阵的初等变换，给出了两个多项式的最小公倍式、最大公因式及其系数多项式的统一求法。

6.A probabilistic algorithm for factoring univariate polynomials over finite fields is presented.

本文给出了有限域上单变元多项式分解的一种概率算法。

7.The conventional methods do not work in practice when dealing with large polynomials because of their high complexity.

在计算实践中，处理大型多项式时，由于复杂性原因，实闭域一阶理论判定方法实际上无效。

8.Factoring polynomials can help simplify complex expressions and solve equations more easily.

因式分解多项式可以帮助简化复杂表达式，并更容易地解决方程。

9.You can add or subtract polynomials by combining like terms.

你可以通过合并同类项来加减多项式。

10.Graphing polynomials allows us to visualize their behavior and find their roots.

绘制多项式的图形可以让我们直观地了解它们的行为并找到它们的根。

11.In algebra, we often work with polynomials, which are expressions consisting of variables raised to whole number powers.

在代数中，我们经常处理多项式，它是由变量的整数次幂组成的表达式。

12.The degree of a polynomial is determined by the highest power of its variable.

一个多项式的次数由其变量的最高幂决定。

作文

Polynomials are a fundamental concept in algebra and mathematics as a whole. A polynomial (多项式) is an expression that consists of variables raised to whole number exponents, combined using addition, subtraction, or multiplication. For example, the expression 2x^2 + 3x - 5 is a polynomial (多项式) in the variable x. The study of polynomials (多项式) is crucial for understanding more complex mathematical concepts, such as functions, equations, and calculus.Throughout history, polynomials (多项式) have played a significant role in various fields, including physics, engineering, and economics. They are used to model real-world scenarios where relationships between quantities can be expressed mathematically. For instance, in physics, the trajectory of a projectile can often be represented by a polynomial (多项式), allowing scientists to predict its path under the influence of gravity. Similarly, in economics, polynomials (多项式) can be used to model cost functions or revenue projections based on different variables.One of the key features of polynomials (多项式) is their degree, which is determined by the highest exponent of the variable present in the expression. The degree of a polynomial (多项式) provides insight into its behavior and the number of possible roots it may have. For example, a first-degree polynomial (多项式) is linear, meaning it will graph as a straight line, while a second-degree polynomial (多项式) is quadratic and will graph as a parabola. Understanding the degree of polynomials (多项式) helps mathematicians and students alike to analyze their properties and solve equations.Moreover, polynomials (多项式) can be classified into different types, such as monomials, binomials, and trinomials, based on the number of terms they contain. A monomial has one term, a binomial has two, and a trinomial has three. This classification aids in simplifying polynomials (多项式) and performing operations such as addition, subtraction, and multiplication. For example, when adding two polynomials (多项式), like (2x^2 + 3x) and (4x^2 - x), we combine like terms to simplify the expression into a single polynomial (多项式).The process of factoring polynomials (多项式) is another important aspect of working with these expressions. Factoring involves breaking down a polynomial (多项式) into simpler components, which can make solving equations easier. For instance, the polynomial (多项式) x^2 - 5x + 6 can be factored into (x - 2)(x - 3), revealing its roots at x = 2 and x = 3. This ability to factor polynomials (多项式) is invaluable in algebra, as it allows for the simplification of complex problems.In conclusion, polynomials (多项式) are a vital part of mathematics that serve as the building blocks for many advanced topics. Their applications in various fields highlight their importance in both theoretical and practical contexts. By mastering the concepts surrounding polynomials (多项式), students can enhance their mathematical skills and prepare themselves for more challenging subjects in the future. Understanding how to manipulate and analyze polynomials (多项式) is not only essential for academic success but also for real-world problem-solving.

多项式是代数和整个数学中一个基本概念。多项式（polynomial）是由变量升至整数指数的表达式，通过加法、减法或乘法结合在一起。例如，表达式 2x^2 + 3x - 5 是一个关于变量 x 的 多项式（polynomial）。研究 多项式（polynomial）对于理解更复杂的数学概念，如函数、方程和微积分至关重要。在历史上，多项式（polynomial）在物理学、工程学和经济学等各个领域都发挥了重要作用。它们用于建模现实世界场景，其中数量之间的关系可以用数学表示。例如，在物理学中，抛射物的轨迹通常可以用一个 多项式（polynomial）来表示，从而使科学家能够预测其在重力影响下的路径。同样，在经济学中，多项式（polynomial）可用于根据不同变量建模成本函数或收入预测。多项式（polynomial）的一个关键特征是其次数，由表达式中变量的最高指数决定。多项式（polynomial）的次数提供了对其行为的洞察以及它可能拥有的根的数量。例如，一次 多项式（polynomial）是线性的，意味着它将图形化为一条直线，而二次 多项式（polynomial）是二次曲线，将图形化为抛物线。理解 多项式（polynomial）的次数有助于数学家和学生分析其属性并解决方程。此外，多项式（polynomial）可以根据包含的项数进行分类，例如单项式、双项式和三项式。单项式有一项，双项式有两项，而三项式有三项。这种分类有助于简化 多项式（polynomial）并执行加法、减法和乘法等运算。例如，当将两个 多项式（polynomial）相加时，如 (2x^2 + 3x) 和 (4x^2 - x)，我们结合同类项以将表达式简化为一个单一的 多项式（polynomial）。因式分解 多项式（polynomial）是处理这些表达式的另一个重要方面。因式分解涉及将 多项式（polynomial）分解为更简单的组成部分，这可以使解决方程变得更容易。例如，多项式（polynomial）x^2 - 5x + 6 可以因式分解为 (x - 2)(x - 3)，揭示其在 x = 2 和 x = 3 的根。在代数中，这种因式分解 多项式（polynomial）的能力是无价的，因为它允许简化复杂问题。总之，多项式（polynomial）是数学中至关重要的一部分，它们作为许多高级主题的构建块。它们在各个领域的应用突显了它们在理论和实践背景中的重要性。通过掌握围绕 多项式（polynomial）的概念，学生可以增强他们的数学技能，为未来更具挑战性的学科做好准备。理解如何操作和分析 多项式（polynomial）不仅对学术成功至关重要，而且对现实世界的问题解决也至关重要。