PrerequisitesPrerequisite

Factoring quadratics - in the form

Factor 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 parentheses.

Example 1

Factor 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

Factor 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 factor into parentheses with integer coefficients.

Your turn

5 practice questions
Question 1

Factor 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

Factor 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

Factor 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

Factor 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

Factor 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