Factorisation is like breaking a big LEGO creation into smaller blocks so you can see how it was built. Instead of one big structure, you figure out the smaller pieces that fit together to make it.
A simple example is the number 15. You can break it into smaller pieces like 3×5, because multiplying 3 and 5 gives you 15.
Purpose of factorisation
The purpose of factorization is to simplify mathematical expressions or solve problems more easily. It’s a powerful tool in math with many practical uses, such as:
1. Solving Equations
Factorisation helps us solve equations by breaking them into simpler parts. For example:
x2 + 5x + 6 = 0
Factoring it into ( x + 2 )( x + 3 ) = 0 lets us find the solutions: x = −2 and x = −3.
2. Simplifying Fractions
Factorisation/ allows us to cancel out common terms in fractions. For example:
Factorising x2 − 9 into ( x − 3 )( x + 3 ) gives:
3. Understanding Numbers and Patterns
In numbers, factorisation helps us see the building blocks (like prime factors). For example, the prime factors of 30 are 2 × 3 × 5. This is useful in areas like cryptography or finding common multiples.
4. Making Complex Problems Easier
Factorisation breaks big, complicated expressions into smaller, manageable parts. This simplifies calculations and makes it easier to see relationships between numbers or variables.
Methods to Factorising a Quadratic Equation
- Cross Method (Factorisation Table)
- Multiplication Frame
- Factoring Quadratics without Guess and Check
1. Cross Method (Factorisation Table)
To solve for x2 + 5x + 6:
2. Factoring Quadratics without Guess and Check
Previously, we were taught to look at the quadratic equation to look at