What is factorising in the context of Edexcel IGCSE Mathematics?

Factorising is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression. In the Edexcel IGCSE Mathematics curriculum, factorising is an essential skill used to simplify equations and solve quadratic equations.

How do you factorise a quadratic expression in Edexcel IGCSE Mathematics?

To factorise a quadratic expression of the form ax^2 + bx + c, you need to find two numbers that multiply to ac and add to b. Once these numbers are identified, you can rewrite the middle term and factor by grouping. This method is crucial for solving quadratic equations in the Edexcel IGCSE syllabus.

What is the difference between factorising and expanding in Mathematics?

Factorising involves breaking down an expression into its factors, while expanding is the process of multiplying factors to form an expression. In the Edexcel IGCSE Mathematics curriculum, students learn both skills to manipulate and solve equations effectively.

Why is factorising important in solving equations in Edexcel IGCSE Mathematics?

Factorising is important because it simplifies complex equations, making them easier to solve. For instance, factorising a quadratic equation allows you to set each factor to zero and solve for the variable. This technique is a fundamental part of the Equations, Formulae and Identities topic in the Edexcel IGCSE Mathematics course.

Can you provide an example of factorising a simple algebraic expression?

Certainly! Consider the expression x^2 - 5x + 6. To factorise, find two numbers that multiply to 6 and add to -5. These numbers are -2 and -3. Rewrite the expression as (x - 2)(x - 3). This factorised form is useful for solving equations and is a key skill in the Edexcel IGCSE Mathematics curriculum.

Equations, Formulae and IdentitiesEdexcel IGCSE Mathematics (4MA1)

Factorising

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Study Notes

Factorisation involves rewriting an algebraic expression by taking out common factors, which is the reverse process of expansion.

Factorisation — the process of expressing an algebraic expression as a product of its factors. Example: x^2 + x = x(x+1)
Common Factor — a factor that is common to all terms in an expression. Example: In 8x^2y + 6xy^2, 2xy is the common factor.
Quadratic Factorisation — rewriting a quadratic expression in the form ax^2 + bx + c as a product of two binomials. Example: x^2 + 11x + 24 = (x+3)(x+8)

Exam Tips

Key Definitions to Remember

Factorisation is the reverse of expansion.
A common factor is a factor shared by all terms in an expression.

Common Confusions

Forgetting to take out the highest common factor (HCF) first.
Mixing up the steps for factorising quadratics with simple factorisation.

Typical Exam Questions

How do you factorise 32p^2q - 4pq^2? Answer: 4pq(8p - q)
How do you factorise 36x^3 + 24x^5? Answer: 12x^3(3 + 2x^2)
How do you factorise 2x^2 + 7x + 5? Answer: (2x + 5)(x + 1)

What Examiners Usually Test

Ability to identify and factor out the common factor.
Correctly factorising quadratic expressions into two binomials.

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