Solving quadratics by factorising

Once a quadratic expression has been factorised, it can be used to solve the quadratic equation (when the expression is equal to zero).

If the product of two factors is equal to zero, then at least one of the factors must be equal to zero. This is called the zero product property.

In other words, one of the brackets needs to be zero if they need to multiply to give zero.

Example: solve

• Factorise the left-hand side:
• Using the zero product property, set each factor equal to zero:
  • or
• Solve :
• Solve :
• Answer: or .

Example: solve

• Factorise the left-hand side:
• Using the zero product property, set each factor equal to zero:
  • or
• Solve :
• Solve :
• Answer: or .