Factorisation Made Easy: Breaking Math into Simpler Parts

Have you ever taken something apart to see how it works? Maybe you’ve opened a toy or pulled apart building blocks to understand how they’re put together. That’s exactly what factorisation is in math—it’s about breaking numbers or expressions into smaller, simpler pieces to understand them better.

What is Factorisation?

Factorisation is a fancy word for finding numbers or expressions that multiply together to make another number or expression. These smaller pieces are called factors.

For example:

• The number 12 can be written as 3 × 4 or 2 × 6. These pairs of numbers are factors of 12.
• If we keep going, we can write 12 as 2 × 2 × 3. These are called prime factors, which means they can’t be broken down further.

In algebra (math with letters and numbers), factorisation is the process of rewriting expressions in a simpler way by finding common parts.

Why Do We Factorise?

1. It simplifies problems.
   Factorising can make a big, complicated math problem much easier to solve.
2. It helps solve equations.
   If you want to figure out the value of x in an equation like x² + 5x + 6 = 0, factorisation is often the first step.
3. It reveals patterns.
   Factorisation helps you see the hidden building blocks of numbers and expressions.

How to Factorise Numbers

Let’s take a number, like 24, and factorise it.

1. Start by thinking about what numbers multiply to give 24:
   • 1 × 24
   • 2 × 12
   • 3 × 8
   • 4 × 6
2. If you keep breaking these numbers down, you’ll get the smallest factors:
   • 2 × 2 × 2 × 3 (prime factors)

This tells us that 24 is built from three 2s and one 3!

Factorising Algebraic Expressions

Now let’s move to algebra. Say we have 6x + 9. How do we factorise it?

1. Look for something common in both parts:
   Both 6x and 9 can be divided by 3.
2. Factor out the common part (this means taking it out like a common ingredient):
   6x + 9 = 3(2x + 3)

That’s it! The expression is now factorised. We’ve rewritten it as a simpler product: 3 and (2x + 3).

What About Quadratic Expressions?

Sometimes, we need to factorise something a bit more complicated, like a quadratic expression:
x² + 5x + 6

Here’s how to do it:

1. Find two numbers that multiply to the last number (6) and add to the middle number (5).
   • The numbers are 2 and 3, because 2 × 3 = 6 and 2 + 3 = 5.
2. Rewrite the expression using these numbers:
   x² + 5x + 6 = (x + 2)(x + 3)

Now it’s factorised! If you multiply it back, you’ll get the original expression.

Real-Life Connection

Factorisation is like finding the recipe for a dish. Imagine you have a chocolate cake, and someone asks, “What’s in it?” You’d say:
“It’s made of flour, sugar, cocoa, and eggs.”

In math, factorisation is like saying:
“12 is made of 2 × 2 × 3” or “6x + 9 is made of 3 × (2x + 3).”

Practice Time!

Here are some problems to try:

1. Factorise the number 36 into its prime factors.
2. Factorise the expression 4x + 12.
3. Factorise the quadratic expression x² + 7x + 10.

Wrapping Up

Factorisation is a superpower in math! It helps you break down big numbers and complicated expressions into smaller, simpler parts. Whether you’re working with plain numbers or algebra, factorisation makes math easier and more fun to solve. Keep practicing, and soon you’ll be the go-to factorisation expert in your class! 🎉