Solving quadratics by factorising

Solving quadratic equations by factorising is one of the key algebraic skills at GCSE. A quadratic equation has the form ax² + bx + c = 0. **The Method:** 1. Rearrange to get zero on one side: ax² + bx + c = 0 2. Factorise the quadratic expression 3. Set each factor equal to zero 4. Solve each simple equation **Why This Works:** If two things multiply to give zero, one of them must be zero. If (x - 2)(x + 3) = 0, then either x - 2 = 0 or x + 3 = 0 **Example:** Solve x² + 5x + 6 = 0 Step 1: Factorise: (x + 2)(x + 3) = 0 Step 2: Set each factor to zero: x + 2 = 0 → x = -2 x + 3 = 0 → x = -3 Solutions: x = -2 or x = -3 **Types of Quadratic:** - **x² + bx + c = 0:** Find two numbers that multiply to c and add to b - **ax² + bx + c = 0:** Use grouping method or trial and improvement - **x² - k = 0:** Difference of two squares: x² = k, so x = ±√k **Checking Solutions:** Substitute each solution back into the original equation. **Exam Tips:** - Always rearrange to = 0 first - Look for common factors before factorising - Quadratics usually have TWO solutions - Check both answers by substitution