trinomials
简明释义
英[ˌtraɪˈnəʊmaɪəlz]美[ˌtraɪˈnoʊmaɪlz]
[数] 三项式
英英释义
单词用法
分解三项式 | |
求解三项式 | |
二次三项式 | |
完全平方三项式 |
同义词
反义词
单项式 | 单项式只包含一个项。 | ||
二项式 | Binomials are often used in algebra to simplify expressions. | 二项式常用于代数中简化表达式。 |
例句
1.Moreover, the period and linear complexity of the generated sequence based on primitive trinomials and quarternomials of degree nover GF(3) are discussed.
进一步讨论了基于GF(3)上本原三项式和四项式的自缩序列的周期和线性复杂度。
2.Moreover, the period and linear complexity of the generated sequence based on primitive trinomials and quarternomials of degree nover GF(3) are discussed.
进一步讨论了基于GF(3)上本原三项式和四项式的自缩序列的周期和线性复杂度。
3.In algebra, we often work with trinomials to factor them into simpler expressions.
在代数中,我们经常处理三项式,将它们因式分解成更简单的表达式。
4.A common example of a trinomial is x² + 5x + 6.
一个常见的三项式例子是 x² + 5x + 6。
5.When graphing, trinomials can create parabolic shapes.
在绘图时,三项式可以形成抛物线形状。
6.Students learn to identify trinomials in their math classes.
学生在数学课上学习识别三项式。
7.To solve a quadratic equation, you may need to use trinomials.
要解二次方程,你可能需要使用三项式。
作文
In mathematics, particularly in algebra, the term trinomials refers to an expression that consists of three distinct terms. These expressions can be quite versatile and are fundamental in various areas of math, including polynomial equations, factoring, and graphing functions. Understanding trinomials is essential for students as they advance in their mathematical studies and encounter more complex concepts. To illustrate the significance of trinomials, let’s consider a simple example: the expression x² + 5x + 6. This expression is a classic case of a trinomial, where each part has a different degree. The first term, x², is the quadratic term; the second term, 5x, is linear; and the last term, 6, is a constant. Each of these components plays a crucial role in the behavior of the entire expression. One of the key operations involving trinomials is factoring. Factoring a trinomial allows us to rewrite it as a product of simpler expressions, which can make solving equations much easier. For instance, the trinomial x² + 5x + 6 can be factored into (x + 2)(x + 3). This not only simplifies the expression but also provides insights into its roots, or the values of x that make the equation equal to zero. In this case, the roots are x = -2 and x = -3. The ability to factor trinomials is a vital skill in algebra, as it lays the groundwork for solving quadratic equations. Students often learn various methods to factor trinomials, such as the trial and error method, the use of the quadratic formula, or completing the square. Each approach has its advantages, and being proficient with them enables students to tackle a wide range of problems effectively. Moreover, trinomials appear frequently in real-world applications. For example, in physics, the trajectory of a projectile can be modeled using a quadratic function, which is essentially a trinomial. Understanding how to manipulate these expressions is crucial for predicting outcomes and analyzing motion. In addition to their practical applications, trinomials also play a significant role in calculus. When dealing with functions, one often encounters trinomials when finding derivatives or integrals. A solid grasp of how these expressions behave is necessary for students who wish to pursue advanced studies in mathematics or related fields. Furthermore, the concept of trinomials extends beyond simple algebraic manipulation. It serves as a gateway to more abstract mathematical concepts, such as polynomial functions and their characteristics. As students progress, they learn to analyze the graphs of trinomials, discerning features like vertex, axis of symmetry, and intercepts. This graphical understanding enhances their overall mathematical intuition and problem-solving skills. In conclusion, trinomials are a fundamental building block in the study of mathematics. They not only serve as important expressions in algebra but also have far-reaching implications in various scientific fields. Mastering trinomials equips students with the tools necessary to tackle more complex mathematical challenges and apply their knowledge in practical situations. Therefore, investing time in understanding trinomials is an invaluable step in any student’s educational journey.
在数学中,特别是在代数中,术语trinomials指的是由三个不同项组成的表达式。这些表达式非常多才多艺,并且在数学的各个领域中都是基础,包括多项式方程、因式分解和图形绘制。理解trinomials对于学生在数学学习中向更复杂的概念进阶至关重要。 为了说明trinomials的重要性,让我们考虑一个简单的例子:表达式x² + 5x + 6。这个表达式是trinomial的经典案例,其中每一部分都有不同的次数。第一项x²是二次项;第二项5x是线性项;最后一项6是常数。这些组成部分在整个表达式的行为中发挥着至关重要的作用。 涉及trinomials的关键操作之一是因式分解。因式分解trinomial使我们能够将其重写为简单表达式的乘积,这可以使求解方程变得更加容易。例如,trinomial x² + 5x + 6 可以因式分解为(x + 2)(x + 3)。这不仅简化了表达式,而且提供了对其根的见解,即使方程等于零的x值。在这种情况下,根是x = -2和x = -3。 因式分解trinomials的能力是代数中的一项重要技能,因为它为解决二次方程奠定了基础。学生通常学习各种方法来因式分解trinomials,例如试错法、使用二次公式或完成平方。每种方法都有其优点,熟练掌握这些方法使学生能够有效地应对各种问题。 此外,trinomials在现实世界应用中经常出现。例如,在物理学中,抛射物的轨迹可以用二次函数建模,实际上就是一个trinomial。理解如何处理这些表达式对于预测结果和分析运动至关重要。 除了实际应用,trinomials在微积分中也发挥着重要作用。在处理函数时,通常会遇到trinomials,当寻找导数或积分时。对这些表达式的行为有扎实的掌握是希望追求高级数学或相关领域的学生的必要条件。 此外,trinomials的概念超越了简单的代数运算。它作为通往更抽象数学概念的门户,如多项式函数及其特征。随着学生的进步,他们学习分析trinomials的图形,识别顶点、对称轴和截距等特征。这种图形理解增强了他们整体的数学直觉和解决问题的能力。 总之,trinomials是数学学习中的一个基础构件。它们不仅作为代数中的重要表达式存在,还在各个科学领域具有深远的影响。掌握trinomials为学生提供了应对更复杂数学挑战和在实际情况中应用知识的工具。因此,花时间理解trinomials是任何学生教育旅程中不可或缺的一步。
文章标题:trinomials的意思是什么
文章链接:https://www.liuxue886.cn/danci/484088.html
本站文章均为原创,未经授权请勿用于任何商业用途
发表评论