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.

Factorising | Edexcel IGCSE Mathematics

Summary and Exam Tips for Factorising

Factorising is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. Factorisation involves breaking down algebraic expressions into simpler components. The primary objective is to learn how to factorise expressions where all terms have common factors and to determine the Highest Common Factor (HCF).

Factorisation is essentially the reverse process of expansion. For example, the expression $2x(3x + y - 4z)$ expands to $6x^2 + 2xy - 8xz$ . Conversely, factorising involves identifying and extracting common factors from expressions, such as $x^2 + x = x(x+1)$ , where $x$ is common to both terms.

When factorising quadratics, the expression is generally in the form $ax^2 + bx + c$ . The process involves finding two numbers that multiply to give $c$ and add to give $b$ . For instance, $x^2 + 11x + 24$ can be factorised to $(x+3)(x+8)$ .

Practice and past paper questions are crucial for mastering factorisation, as they help reinforce the concept of dividing terms into pairs and extracting common factors.

Exam Tips

Identify Common Factors: Always start by identifying the HCF of the terms in the expression. This simplifies the factorisation process.
Pair Terms Wisely: Sometimes, dividing terms into pairs can make it easier to spot common factors. Practice this technique with different expressions.
Quadratic Factorisation: For quadratics, remember to find two numbers that multiply to the constant term and add to the coefficient of the linear term.
Check Your Work: After factorising, expand the brackets to ensure you get back the original expression. This helps verify your solution.
Practice Regularly: Use past paper questions to familiarize yourself with different types of factorisation problems and improve your speed and accuracy.

Factorising

Exam Tips and Study Notes for Factorising