Factorising
Understanding Factorising
- Factorising is the process of breaking down an algebraic expression into its simplest form, involving its factors.
- A factor is a number or algebraic term that divides into another number or term without leaving a remainder.
- Factorising often involves handling expressions having multiple terms, often linked by multiplication.
Basic Factorising
- To factorise a simple expression, start by identifying the highest common factor (HCF) of the terms involved. This is a number that divides evenly into all terms.
- For example, in the expression 4x + 8, the HCF is 4.
- Once the HCF is identified, you divide every term in the expression by the HCF and write the expression as the product of the HCF and the remaining terms.
- Using the example above, the factorised form would be 4(x + 2).
Factorising Quadratics
- For quadratic equations in the form ax² + bx + c, factorisation involves breaking it down into two binomial expressions.
- The quadratic can be factorised into the form (px + q)(rx + s), where px and rx are the factors of ax², and q and s are the factors of c.
- Be sure that the product of pr equals to a and qs equals to c, and the sum of ps and qr equals to b.
- Practice is essential for getting comfortable with factorising quadratics.
Common Mistakes when Factorising
- One big pitfall when factorising is failing to identify the correct HCF, especially in expressions involving both numbers and variables.
- A common mistake when factorising quadratics is choosing the wrong pairs of numbers for the binomials, causing the products and sum not to match the original quadratic terms.
- Be careful not to overlook negative signs when factorising. Remember, a negative sign belongs to the term it directly precedes. For instance, in the expression 2x - 4, -4 is one of the terms.
- In quadratic factorisation, be wary of missing solutions. Sometimes both binomial expressions can be further factorised. Always check for this possibility to avoid losing marks.