Understanding the Basics of Factorisation
To begin with, let's understand what factorisation is all about. When we have an algebraic expression, we can break it down into its prime factors, which are the simplest building blocks that cannot be further divided. For example, the expression 6 can be broken down into its prime factors as 2 x 3. The factorisation formula is based on this concept, and it helps us to simplify expressions by finding their prime factors. The factorisation formula is based on the idea of finding the greatest common factor (GCF) of two or more numbers. The GCF is the largest number that divides both numbers without leaving a remainder. For example, the GCF of 12 and 15 is 3, because 3 is the largest number that divides both 12 and 15 without leaving a remainder.Step-by-Step Guide to Applying the Factorisation Formula
Applying the factorisation formula involves several steps. Here's a step-by-step guide to help you master this skill:- Identify the expression you want to factorise.
- Look for common factors in the expression.
- Identify the greatest common factor (GCF) of the expression.
- Check if the GCF can be further divided into prime factors.
- Write the expression as a product of its prime factors.
- Identify the expression: 12x^2 + 18x
- Look for common factors: 6 is the common factor, as both 12 and 18 are divisible by 6.
- Identify the GCF: 6 is the GCF, as it is the largest number that divides both 12 and 18 without leaving a remainder.
- Check if the GCF can be further divided: 6 can be divided into 2 x 3, so we can further divide it into prime factors.
- Write the expression as a product of its prime factors: 6x(2x + 3).
Practical Tips and Tricks
- Start by identifying the greatest common factor (GCF) of the expression. This will help you simplify the expression.
- Look for common factors in the expression. This will help you identify the GCF.
- Check if the GCF can be further divided into prime factors. This will help you write the expression as a product of its prime factors.
- Use the distributive property to simplify the expression. This will help you identify the GCF and write the expression as a product of its prime factors.
- Practice, practice, practice! The more you practice, the more comfortable you will become with applying the factorisation formula.
Comparing Different Factorisation Formulas
The factorisation formula is not the only factorisation formula available. Here's a table comparing different factorisation formulas:| Formula | Description | Example |
|---|---|---|
| Factorisation Formula | Breaks down an expression into its prime factors. | 12x^2 + 18x = 6x(2x + 3) |
| Algebraic Factorisation | Uses algebraic techniques to factorise an expression. | (x + 3)(x - 2) = x^2 + x - 6 |
| Polynomial Factorisation | Uses polynomial techniques to factorise an expression. | (x^2 + 4)(x - 2) = x^3 - 2x^2 + 4x - 8 |