IGCSE Maths Teacher’s Guide 400: Quadratic Equations by Factorisation | IGCSE 数学教师用书 400：用因式分解法解二次方程

📚 IGCSE Maths Teacher’s Guide 400: Quadratic Equations by Factorisation | IGCSE 数学教师用书 400：用因式分解法解二次方程

This Teacher’s Guide 400 resource focuses on one of the most important algebra skills in IGCSE Mathematics: solving quadratic equations by factorisation. Many exam questions, from short one-mark checks to multi-step problems, require you to factorise a quadratic expression quickly and accurately.

本教师用书 400 资源聚焦 IGCSE 数学中最重要的代数技能之一：用因式分解法解二次方程。许多考试题目，从一分的快速检查到多步骤综合题，都要求你快速且准确地对二次式进行因式分解。

1. Learning Objectives | 学习目标

By the end of this guide, you should be able to recognise a quadratic equation, write it in standard form, factorise it, and use the zero-product property to find all solutions.

学完本指南后，你应当能够识别二次方程，将它写成标准形式，进行因式分解，并利用零积性质求出所有解。

You should also be able to check your answers by substituting them back into the original equation and to choose the most efficient method for different types of quadratics.

你还应当能够将答案代回原方程进行检验，并能针对不同类型的二次式选择最高效的方法。

In addition, you should know when factorisation is not possible using integers, so you can decide whether to use the quadratic formula or completing the square instead. This judgement is frequently tested in IGCSE papers.

此外，你还应当知道什么时候二次式不能用整数进行因式分解，从而决定是否改用二次公式或配方法。这种判断在 IGCSE 试卷中经常出现。

2. Prerequisite Knowledge Check | 预备知识自检

Before working through this guide, make sure you can expand double brackets confidently. For example, (x + 2)(x + 3) expands to x² + 5x + 6.

在学习本指南之前，请确保你能熟练展开双重括号。例如，(x + 2)(x + 3) 展开后得到 x² + 5x + 6。

You should also know how to find factor pairs of a number, including negative factor pairs, and how to solve a simple linear equation such as x + 3 = 0.

你还应当知道如何找出一个数的因数对，包括负因数对，以及如何解简单的一元一次方程，例如 x + 3 = 0。

If any of these skills feel weak, revise them first because factorising quadratics reverses the expansion process and relies heavily on sign rules.

如果这些技能中有任何一项不够熟练，请先复习，因为二次式的因式分解是展开的逆过程，并且高度依赖符号法则。

For example, when we expand (x – 2)(

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