Year 9: Solve the quadratic equation by factorisation

What is Factorisation?

Factorisation is a method to solve quadratic equations (equations in the form ax² + bx + c = 0) by breaking down the expression into a product of simpler expressions (factors).

Steps for Solving by Factorisation

1. Rearrange the Equation: Make sure the equation is in the standard form: ax² + bx + c = 0
2. Factor the Quadratic Expression: Find two binomials that, when multiplied, give you the original quadratic expression. This is often the trickiest part. Look for factors of 'a' and 'c' that add up to 'b'.
3. Set each factor to zero: Once you've factored, set each factor equal to zero. For example, if you have (x + 3)(x - 2) = 0, then you set: x + 3 = 0 and x - 2 = 0
4. Solve for x: Solve each of the resulting linear equations for x.

Examples

Example 1: x² + 5x + 6 = 0 factors to (x + 2)(x + 3) = 0. Therefore, x = -2 or x = -3

Example 2: 2x² - 7x + 3 = 0 factors to (2x - 1)(x - 3) = 0. Therefore, x = 1/2 or x = 3

Important Note

This method works best when the quadratic expression can be easily factored. If it cannot be easily factored, you will need to use other methods like the quadratic formula.