PrerequisitesPrerequisite

Factorising quadratics - in the form

Factorise the quadratic using the key steps.

  • Multiply the coefficient of by the constant to find the required product.
  • Find a pair with this product and a sum equal to the coefficient of , then split the middle term.

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
Take out any common numerical factor before using this method.

Your turn

5 practice questions
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. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair