EDEXCEL GCSE FOUNDATION MATHS - What are Factorising

Edexcel GCSE Foundation Maths: Factoring

What are Factors?

Factors are numbers that divide evenly into another number. For example, the factors of 12 are:

What is Factoring?

Factoring is the process of breaking down a number or an algebraic expression into its factors.

Factoring Expressions:

Finding the Highest Common Factor (HCF):
- Step 1: Identify the common factors of all the terms in the expression.
- Step 2: Find the highest common factor (HCF).
- Step 3: Divide each term in the expression by the HCF.
- Step 4: Write the HCF outside brackets and the results of the division inside the brackets.
Example: Factorise 6x + 9
- Step 1: Common factors are 3 and 1.
- Step 2: HCF is 3.
- Step 3: 6x/3 = 2x and 9/3 = 3
- Step 4: 6x + 9 = 3(2x + 3)
Factoring Quadratics:
- Step 1: Identify the coefficients of the quadratic expression (a, b, and c in ax² + bx + c).
- Step 2: Find two numbers that multiply to give 'ac' and add up to 'b'.
- Step 3: Rewrite the middle term (bx) using the two numbers found in step 2.
- Step 4: Factorise the expression by grouping the terms.
Example: Factorise x² + 5x + 6
- Step 1: a = 1, b = 5, c = 6
- Step 2: Two numbers that multiply to 6 and add to 5 are 2 and 3.
- Step 3: x² + 5x + 6 = x² + 2x + 3x + 6
- Step 4: x² + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 2)(x + 3)

Why Factoring is Important:

Factoring is an important skill in algebra as it allows us to:

Simplify expressions: Factoring can make expressions easier to work with and solve.
Solve equations: Factoring can be used to solve quadratic equations.
Analyze functions: Factoring can help us understand the behavior of polynomial functions.

Practice Exercises:

Remember: Practice makes perfect! The more you practice factoring, the easier it will become.