Solving Quadratics by Factorising | Mathematics for GCSE/IGCSE - Class 10 PDF Download

How do I solve a quadratic equation using factorisation?

• Rearrange the expression into the form ax² + bx + c = 0, ensuring zero is on one side. It's preferable to use the side where 𝑎a is positive.
• Factorize the quadratic equation and solve each bracket by setting it equal to zero. For instance, if (x + 4)(x − 1) = 0, then either x + 4 = 0 or x − 1 = 0, as when A × B = 0, either A = 0 or B = 0.
• To solve (x − 3)(x + 7) = 0:
  • Solve "first bracket = 0": x − 3 = 0, so x = 3.
  • Solve "second bracket = 0": x + 7 = 0, giving x = −7.
  • Thus, the solutions are x = 3 or x = −7, with the solutions having opposite signs to the numbers in the brackets.

• To solve (2x − 3)(3x + 5) = 0:
  • Solve "first bracket = 0": 2x − 3 = 0, leading to x = 3/2.
  • Solve "second bracket = 0": 3x + 5 = 0, yielding x = .
  • Hence, the solutions are
• To solve x(x − 4) = 0:
  • Think of x as (x − 0) or x.
  • Solve "first bracket = 0": x = 0.
  • Solve "second bracket = 0": x − 4 = 0, which gives x=4.
  • Therefore, the solutions are x = 0 or x = 4.
• Avoid dividing both sides by x initially, as it can lead to a loss of solutions (in this case, x = 0).