factorization

简明释义

英[ˌfæktəraɪˈzeɪʃən]美[ˌfæktərəˈzeɪʃən]

n. [数] 因子分解；[数] 因式分解

英英释义

单词用法

同义词

反义词

例句

1.Public key RSA mainly depends on the establishment of the factorization difficulty of a big integer.

公钥密码算法RS A主要是依赖于大数的因数分解的困难性建立的。

2.Methods A simple method for distinguishing of exponential distribution family is obtained based on factorization theorem.

方法在因子分解定理的基础上提出了一个判别指数型分布族的简单方法。

3.The problems are closelurelated with factorization problems for rational matrix functions.

这类问题与矩阵函数因子分解有着密切联系。

4.VB Math Example: prime factorization source code, there is need for the next.

说明：VB数学运算实例：分解质因数源代码，有需要的下。

5.Two methods area optimizing factorization to decrease the error of rounding operations.

优化因式分解，以减少取整误差的引入。

6.The safe of RSA algorithm based on difficulty in the large number factorization.

RSA算法的安全性依赖于大数的因数分解的困难性。

7.The scheme's security is based on the computing difficulty of solving the Factorization Problem and the Discrete Logarithm Problem.

该方案的安全性取决于求解因子分解问题与离散对数问题的计算难度。

8.The process of finding the prime factorization 因式分解 of a number is essential in number theory.

找到一个数字的质因数分解因式分解的过程在数论中是至关重要的。

9.In algebra, factorization 因式分解 helps simplify complex expressions.

在代数中，因式分解因式分解有助于简化复杂的表达式。

10.The quadratic formula can be derived from the factorization 因式分解 of a polynomial.

二次公式可以通过多项式的因式分解因式分解推导出来。

11.Students often struggle with the factorization 因式分解 of trinomials.

学生们常常在三项式的因式分解因式分解上遇到困难。

12.Factorization 因式分解 is used in cryptography to secure data.

因式分解因式分解在密码学中用于保护数据安全。

作文

In mathematics, the process of breaking down an expression into a product of its factors is known as factorization. This concept is fundamental in various branches of mathematics, including algebra and number theory. Understanding factorization can significantly simplify complex problems and equations. For instance, when we factor a polynomial, we rewrite it as a product of simpler polynomials, which can make solving equations much easier. Let’s consider a simple example: the quadratic equation x² - 5x + 6. To solve this equation, we can use factorization. We look for two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of the linear term). The numbers -2 and -3 fit these criteria. Therefore, we can express the quadratic as (x - 2)(x - 3) = 0. By setting each factor to zero, we find the solutions x = 2 and x = 3. This is a clear demonstration of how factorization can be used to solve equations efficiently. Moreover, factorization is not only applicable to polynomials but also plays a crucial role in number theory. When we talk about prime factorization, we are referring to expressing a number as a product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7 or 2² × 7. This concept is essential for understanding the properties of numbers and is widely used in cryptography and computer science. In addition to simplifying calculations, factorization helps us understand the structure of mathematical expressions. By examining the factors of a polynomial, we can gain insights into its roots and behavior. For instance, the degree of the polynomial tells us how many times it can intersect the x-axis, which corresponds to the number of real roots it has. Each factor contributes to this understanding, making factorization a powerful tool in analyzing functions. Furthermore, in practical applications, factorization can be used in areas such as physics and engineering. For example, when analyzing forces in equilibrium, we might need to factor expressions to understand the relationships between different forces acting on an object. This shows that factorization is not just an abstract mathematical concept but has real-world implications. In conclusion, factorization is a vital skill in mathematics that allows us to simplify expressions, solve equations, and understand the properties of numbers. Whether we are dealing with polynomials or integers, mastering factorization equips us with the tools necessary to tackle a wide range of mathematical challenges. As students progress in their studies, they will encounter increasingly complex problems where factorization will be an indispensable technique. Thus, developing a strong foundation in factorization is essential for anyone looking to excel in mathematics and related fields.

在数学中，将一个表达式分解为其因子的乘积的过程被称为因式分解。这一概念在代数和数论等多个数学分支中都是基础。理解因式分解可以显著简化复杂的问题和方程。例如，当我们对多项式进行因式分解时，我们将其重写为更简单的多项式的乘积，这可以使求解方程变得更加容易。 让我们考虑一个简单的例子：二次方程x² - 5x + 6。要解决这个方程，我们可以使用因式分解。我们寻找两个数，它们的乘积为6（常数项），并且加起来为-5（线性项的系数）。-2和-3符合这些标准。因此，我们可以将这个二次方程表示为(x - 2)(x - 3) = 0。通过将每个因式设为零，我们找到了解x = 2和x = 3。这清楚地展示了因式分解如何高效地用于求解方程。 此外，因式分解不仅适用于多项式，还在数论中发挥着重要作用。当我们谈论质因数分解时，我们指的是将一个数表示为其质因子的乘积。例如，28的质因数分解为2 × 2 × 7或2² × 7。这个概念对于理解数字的性质至关重要，并广泛应用于密码学和计算机科学。 除了简化计算外，因式分解还帮助我们理解数学表达式的结构。通过检查多项式的因子，我们可以获得关于其根和行为的见解。例如，多项式的次数告诉我们它可以与x轴相交多少次，这对应于它拥有多少个实根。每个因子都对这种理解有所贡献，使得因式分解成为分析函数的强大工具。 此外，在实际应用中，因式分解可以用于物理和工程等领域。例如，在分析平衡中的力时，我们可能需要对表达式进行因式分解，以理解作用在物体上的不同力之间的关系。这表明因式分解不仅是一个抽象的数学概念，而具有现实世界的意义。 总之，因式分解是数学中一项重要的技能，使我们能够简化表达式、求解方程和理解数字的性质。无论我们处理的是多项式还是整数，掌握因式分解为我们提供了解决各种数学挑战所需的工具。随着学生在学习中的进步，他们将遇到越来越复杂的问题，而因式分解将成为一种不可或缺的技术。因此，建立扎实的因式分解基础对于任何希望在数学及相关领域中脱颖而出的人来说都是至关重要的。