Solving Quadratics by Factorising (Cambridge O Level Maths)

How do I solve a quadratic equation using factorisation?

• Rearrange it into the form ax² + bx + c = 0
  • zero must be on one side
    • it is easier to use the side where a is positive
• Factorise the quadratic and solve each bracket equal to zero
  • If (x + 4)(x - 1) = 0, then either x + 4 = 0 or x - 1 = 0
    • Because if A × B = 0, then either A = 0 or B = 0
• To solve
  • …solve “first bracket = 0”:
    • x – 3 = 0 
    • add 3 to both sides: x = 3
  • …and solve “second bracket = 0”
    • x + 7 = 0
    • subtract 7 from both sides: x = -7
  • The two solutions are x = 3 or x = -7
    
    • The solutions have the opposite signs to the numbers in the brackets
• To solve 
  • …solve “first bracket = 0”
    • 2x – 3 = 0
    • add 3 to both sides: 2x = 3
    • divide both sides by 2: x = 
  • …solve “second bracket = 0”
    • 3x + 5 = 0
    • subtract 5 from both sides: 3x = -5
    • divide both sides by 3: x = 
  • The two solutions are x =  or x = 
• To solve
  • it may help to think of x as (x – 0) or (x)
  • …solve “first bracket = 0” 
    • (x) = 0, so x = 0
  • …solve “second bracket = 0”
    • x – 4 = 0
    • add 4 to both sides: x = 4
  • The two solutions are x = 0 or x = 4
    • It is a common mistake to divide both sides by x at the beginning - you will lose a solution (the x = 0 solution)