保理计算器

因式分解计算器是一款免费的在线工具，能助你迅速分解多项式、三项式、二项式及二次方程。它提供分步解决方案，是学生、教师及所有解决代数问题人士的必备工具。

Polynomial Expression

Enter Expression to Factor

x^2 - 4

(x - 2)(x + 2)

x^2 + 5x + 6

(x + 2)(x + 3)

x^3 - 3x + 2

(x - 1)^2(x + 2)

x^4 - 81

(x^2 + 9)(x - 3)(x + 3)

Factoring Results

Factored Form

(x - 2)(x + 2)

Methods

Graph

Difference of Squares

This method applies to expressions of the form a² - b², which factor into (a - b)(a + b).

a² - b² = (a - b)(a + b)

Used for expressions like: x² - 4, 9x² - 16, etc.

Grouping Method

This method involves grouping terms to find common factors. Particularly useful for polynomials with 4 or more terms.

ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

Quadratic Factoring

For quadratic expressions ax² + bx + c, find two numbers that multiply to ac and add to b.

ax² + bx + c = (mx + p)(nx + q)

Where m×n = a, p×q = c, and m×q + n×p = b

Function Graph

Visual representation of the original and factored expressions

Solution Steps

1 Recognize this as a difference of squares: a² - b² = (a - b)(a + b)

2 Rewrite x² - 4 as x² - 2²

3 Apply the formula: x² - 2² = (x - 2)(x + 2)

Supported Formats

Polynomials with one variable (x)
Binomials (e.g. x² - 4)
Trinomials (e.g. x² + 5x + 6)
Higher-degree polynomials
Integer coefficients
Complex expressions may take longer to process

🎨 轻图神器

图片压缩、裁剪、去水印，免费图片处理小程序

🎬 轻影神器

视频去水印、压缩、转格式，免费视频处理小程

🔄 轻转神器

PDF、文档、电子书互转，免费格式转换小程

🧮 轻算神器

房贷、个税、汇率等72种计算，免费实用工具小程

100% browser-based No upload to server Free to use

关于在线计算器的常见问题

如何使用保理计算器？操作复杂吗？

其实很简单！你只需要在输入框里写好你要分解的多项式，比如“x^2 + 5x + 6”，然后点击“计算”。几秒钟后就会出现完整的解答过程，包括使用的因式分解方法（如配方法、分组法、十字相乘法），还有图形展示，帮助你直观理解根的位置和函数行为。

Factoring in Algebra

Factoring is the process of breaking down an expression into a product of simpler expressions. It is a fundamental concept in algebra with several important applications:

Why Factor?

Solving Equations: Factoring helps solve polynomial equations by using the zero product property.
Simplifying Expressions: Complex expressions can be simplified by factoring out common terms.
Graphing Functions: Factored forms reveal the roots (x-intercepts) of polynomial functions.
Calculus: Factoring is useful in limits, derivatives, and integrals.

Common Factoring Techniques

Greatest Common Factor (GCF): Factor out the largest common factor of all terms.
Difference of Squares: a² - b² = (a - b)(a + b)
Perfect Square Trinomials: a² ± 2ab + b² = (a ± b)²
Grouping: Group terms to find common factors in each group.
Quadratic Trinomials: ax² + bx + c = (mx + p)(nx + q)

保理计算器

Polynomial Expression