Algebra and proofAdditional / Further Maths

Solving quadratics by factorising

Set each factor equal to zero after putting the equation in zero form.

  • Rearrange so that one side is zero, then factorise.
  • A product is zero when at least one factor is zero.
  • Solve both linear equations and state both roots.

Example 1

Use the zero-product rule

Solve by factorising.

Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.

Example 2

Find all real solutions by factorising.

Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.

Your turn

Question 1

Find all real solutions.

Check answer
Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 2

Find all real solutions.

Check answer
Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 3

Find all real solutions.

Check answer
Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 4

Find all real solutions.

Check answer
Factorise the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 5

Find all real solutions.

Check answer
Factorise the expression.Set each factor equal to zero, then isolate . Retain every distinct solution.
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