Functions and graphsAdditional / Further Maths

Finding real zeros by factorising

Factorise the polynomial, then solve each factor equal to zero.

  • Take out a common factor first when one is present.
  • Use quadratic factorisation or a supplied factor where appropriate.
  • Keep the zero root when taking out a factor of .

Example 1

Do not lose the zero root

Factorise to find all real zeros.

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

Example 2

Factorise to find all real zeros.

Factorise the expression.Simplify the numerical terms and collect like terms.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.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
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