Algebra and proofAdditional / Further Maths

Factorising quadratics - in the form

Factorise the quadratic using the key steps.

  • Factor out , then use the product and sum inside the bracket.
  • Keep the negative sign outside the two factors.

Example 1

Factorise fully.

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Example 2

Factorise fully.

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Remember
For example, . The minus sign changes all three terms.

Your turn

Question 1

Factorise fully.

Check answer

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair
Question 2

Factorise fully.

Check answer

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair
Question 3

Factorise fully.

Check answer

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled.
NumbersProductSum
Chosen pair
Question 4

Factorise fully.

Check answer

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair
Question 5

Factorise fully.

Check answer

Factor out .

Find two numbers with a product of and a sum of .

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair