factorized

简明释义

英[ˈfæktəraɪzd]美[ˈfæktəraɪzd]

因式分解，把复杂计算分解为基本运算

英英释义

单词用法

同义词

反义词

例句

1.In this paper, we discuss isomorphic factorization for tensor product of two divisible graphs and prove the conditions for the tensor product graphs to be factorized isomorphically.

本文讨论了两个可分图的张量乘积图的同构因子分解问题。

2.In this paper, we discuss isomorphic factorization for tensor product of two divisible graphs and prove the conditions for the tensor product graphs to be factorized isomorphically.

本文讨论了两个可分图的张量乘积图的同构因子分解问题。

3.The equation was successfully factorized into simpler terms.

这个方程成功地被因式分解成更简单的项。

4.In algebra, we often need to factorize polynomials to solve equations.

在代数中，我们经常需要因式分解多项式以解方程。

5.The quadratic expression can be factorized using the roots.

这个二次表达式可以通过根来因式分解。

6.To simplify the problem, the large numbers were factorized into their prime components.

为了简化问题，大数字被因式分解为它们的质因数。

7.After the polynomial was factorized, it was easier to find its zeros.

在多项式被因式分解后，更容易找到它的零点。

作文

In mathematics, the concept of factorization is crucial for simplifying expressions and solving equations. When we say that a number or an expression has been factorized, we mean that it has been broken down into its constituent parts, called factors, which can be multiplied together to yield the original number or expression. For instance, the number 12 can be factorized into 3 and 4, since 3 times 4 equals 12. Similarly, algebraic expressions can be factorized to make them easier to work with. Consider the quadratic expression x² - 5x + 6. This expression can be factorized into (x - 2)(x - 3). By factorizing the expression, we can quickly identify its roots, which are the values of x that make the expression equal to zero. In this case, the roots are x = 2 and x = 3. Understanding how to factorize expressions is not only important for academic purposes but also has practical applications in various fields such as engineering, physics, and economics. For example, in physics, when analyzing forces acting on an object, one may need to factorize equations to determine the net force or to solve for unknown variables. Moreover, factorization plays a significant role in simplifying complex problems. When faced with a challenging mathematical problem, breaking it down into smaller, more manageable parts through factorization can lead to a clearer path to the solution. This technique is particularly useful in calculus, where functions often need to be factorized to find limits, derivatives, or integrals. In computer science, factorization is also an essential concept, especially in algorithms related to cryptography. Many encryption methods rely on the difficulty of factorizing large numbers into their prime factors. The security of these systems hinges on the assumption that while it is easy to multiply two large primes together, factorizing the resulting product back into its original primes is computationally challenging. This principle underlies the security of many online transactions and communications. In summary, the ability to factorize numbers and expressions is a fundamental skill in mathematics that extends beyond the classroom. It aids in problem-solving, enhances our understanding of mathematical relationships, and has wide-ranging applications in various scientific and technological fields. As students progress through their education, mastering the art of factorization will empower them to tackle increasingly complex problems with confidence and clarity. Ultimately, whether in academia, industry, or everyday life, the skill of factorizing plays a pivotal role in our ability to analyze and interpret the world around us. Therefore, it is essential for learners to grasp this concept thoroughly and practice factorizing different types of expressions to build a strong mathematical foundation.

在数学中，因式分解的概念对于简化表达式和解决方程至关重要。当我们说一个数字或表达式被factorized时，我们的意思是它被分解成其组成部分，称为因子，这些因子可以相乘以得到原始数字或表达式。例如，数字12可以被factorized为3和4，因为3乘以4等于12。同样，代数表达式也可以被factorized以使其更易于处理。考虑二次表达式x² - 5x + 6。这个表达式可以被factorized为(x - 2)(x - 3)。通过factorizing这个表达式，我们可以迅速识别出它的根，即使表达式等于零的x值。在这种情况下，根为x = 2和x = 3。 理解如何factorize表达式不仅对学术目的很重要，而且在工程、物理和经济等各个领域都有实际应用。例如，在物理学中，当分析作用于物体上的力时，可能需要factorize方程以确定净力或求解未知变量。 此外，因式分解在简化复杂问题中也发挥着重要作用。当面对一个具有挑战性的数学问题时，通过factorization将其分解为更小、更可管理的部分，可以为解决方案提供更清晰的路径。这种技术在微积分中特别有用，因为函数通常需要被factorized以寻找极限、导数或积分。 在计算机科学中，factorization也是一个重要概念，尤其是在与密码学相关的算法中。许多加密方法依赖于将大数字factorized为其素因子的难度。这些系统的安全性基于这样一种假设：虽然将两个大素数相乘是容易的，但将结果产品factorized回其原始素数是计算上具有挑战性的。这一原理支撑着许多在线交易和通信的安全性。 总之，能够factorize数字和表达式是一项基本的数学技能，它超越了课堂。它有助于解决问题，增强我们对数学关系的理解，并在各个科学和技术领域具有广泛的应用。随着学生在教育过程中的进步，掌握factorization的艺术将使他们能够自信而清晰地应对日益复杂的问题。 最终，无论是在学术界、工业界还是日常生活中，factorizing的技能在我们分析和解释周围世界的能力中发挥着关键作用。因此，学习者必须彻底掌握这一概念，并练习factorizing不同类型的表达式，以建立坚实的数学基础。