Factorising is an essential skill in National 5 Maths, helping students simplify expressions and solve equations efficiently. Many students find factorising tricky at first, but with the right approach, it becomes much easier. In this guide, we’ll break down the key factorisation techniques you need to know, provide step-by-step examples, and highlight common mistakes to avoid. Whether you’re revising for your National 5 exams or just looking to improve your algebra skills, this guide will help you master factorising with confidence.
If you are studying for naitonal 5 exams you’ll want to have a look at our other blog post: How are National 5 exams in Scotland graded?
What is Factorisation?
Factorisation is the process of breaking down an algebraic expression into simpler expressions that, when multiplied together, give the original expression. This is the reverse of expanding brackets.
Common Methods of Factorisation
1. Factorising Common Factors
The simplest way to factorise an expression is by identifying and taking out the highest common factor (HCF) of all the terms.
Example:
Factorise: 6x + 9
- The highest common factor of 6x and 9 is 3.
- Factor out the 3: 3(2x + 3)
2. Factorising Quadratic Expressions
Quadratic expressions take the form ax^2 + bx + c. There are different methods to factorise these, including:
(a) Factorising Simple Quadratics (where a = 1)
Factorise: x^2 + 7x + 10
- Find two numbers that multiply to 10 and add to 7: (5 and 2)
- Write in factorised form: (x + 5)(x + 2)
(b) Factorising Quadratics with a Coefficient of x² (where a ≠ 1)
Factorise: 2x^2 + 7x + 3
- Multiply a and c: 2 × 3 = 6
- Find two numbers that multiply to 6 and add to 7: (6 and 1)
- Rewrite the middle term: 2x^2 + 6x + x + 3
- Factor by grouping: 2x(x + 3) + 1(x + 3)
- Final factorised form: (2x + 1)(x + 3)
3. Difference of Two Squares
This method is used for expressions in the form a^2 – b^2.
Example:
Factorise: x^2 – 16
- Recognise that 16 is a square number: x^2 – 4^2
- Apply the difference of squares formula: (x – 4)(x + 4)
If you want more info on how to use factorisation have a look at the BBC Bitesize website here.
Why is Factorisation Important?
Factorisation is crucial in solving quadratic equations, simplifying algebraic expressions, and understanding graphs of functions. Mastering these techniques will help you in your National 5 Maths exam and beyond.
Factorisation in National 5 Maths Exams
Factorisation is a crucial topic in National 5 Maths exams. You will often encounter questions that require you to factorise expressions as part of solving equations or simplifying algebraic expressions. Here are some common ways factorisation appears in the exam:
- Solving Quadratic Equations: You may need to factorise a quadratic expression to find the values of x that satisfy the equation.
- Simplifying Expressions: Factorising helps simplify expressions, making them easier to work with in later steps.
- Recognising Patterns: Some questions require recognising the difference of two squares or factoring common terms before proceeding to solve.
- Word Problems: Factorisation may be embedded in real-life context problems where algebra is needed to find unknown values.
Practising past exam questions and working on a variety of factorisation problems will help you gain confidence and improve your ability to apply these skills under exam conditions.
Practice Questions
Try these questions to test your understanding:
- Factorise 4x + 12
- Factorise x^2 + 9x + 20
- Factorise 3x^2 + 8x + 4
- Factorise x^2 – 25
Factorisation is a key skill that becomes easier with practice. Keep working through problems, and soon, you’ll be factorising with confidence!
For more National 5 Maths help, check out our tutoring services at Central Tutors!
