保理計算器

因式分解計算器是一個免費的網路工具，能幫助您快速分解多項式、三項式、二項式以及二次方程式。它提供逐步解題方案，是學生、老師以及任何解代數問題人士的必備工具。

Polynomial Expression

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
1

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.

2

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)
3

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
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相關工具 - 更多免費線上計算機

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關於線上計算機的常見問題

保理計算器可以用在手機上嗎？有手機版嗎？

當然可以！這是一個純網頁應用，不需要下載 App，無論你是用 iPhone、Android 還是平板，只要打開瀏覽器就能直接使用。我在捷運上用它解決了一道難題，完全不受限制，操作起來也順手得很。

如何用保理計算器分解 x² + 5x + 6？

這個很常見！你只需要輸入 x^2 + 5x + 6，系統就會自動識別這是「二次三項式」，並找出兩個數字：2 和 3，因為 2×3=6 且 2+3=5。所以答案就是 (x + 2)(x + 3)。這種方式特別適合考試前複習，一看就懂，再也不用背口訣了。

保理計算器支援高次多項式嗎？例如 x³ - 3x + 2？

是的！這正是它的強項之一。像 x³ - 3x + 2，它可以正確分解為 (x - 1)²(x + 2)，並且顯示使用的是「因式定理」結合群組法。即使是很複雜的四次式，如 x⁴ - 81，也能輕鬆處理成 (x² + 9)(x - 3)(x + 3)，非常適合大學微積分或高等數學初學者。

使用保理計算器會不會太慢？處理大題目要等很久嗎？

一般來說不會。除非你輸入極其龐大的多項式（比如超過 10 項），否則幾乎都是秒回。我自己測試過幾十道題，最快不到 1 秒，最久也不超過 5 秒，完全符合現代人追求效率的需求。

保理計算器適合教師教學使用嗎？能當作課堂演示工具嗎？

絕對適合！我認識一位國中數學老師，他每次上課前都會先用這個工具準備好例題，然後投影出來一步一步講解，學生反應超好。不僅節省板書時間，還能確保每個步驟都正確無誤，避免誤導學生。

Guide

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

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