Algebra and proofAdditional / Further Maths

Factorising quadratics - in the form

Factorise the quadratic using the key steps.

  • Find two numbers whose product is the constant and whose sum is the coefficient of .
  • Use the pair in two brackets.

Example 1

Factorise fully.

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

Example 2

Factorise fully.

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
Some quadratics do not factorise into brackets with integer coefficients.

Your turn

Question 1

Factorise fully.

Check answer

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 2

Factorise fully.

Check answer

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 3

Factorise fully.

Check answer

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 4

Factorise fully.

Check answer

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

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