This guide shows the different ways of factorising quadratic expressions by looking for a Highest Common Factor, difference of two squares or a trinomial.
Quadratic expressions have a distinct look about them. They have the form:
ax² + bx + c = 0, where a≠0.
When it comes to factorising a quadratic expression, there are particular methods depending on the form of the expression
In the tutorials which follow, I will show you how to factorise the above expressions.
Highest common factor HCF types
Your first priority in factorising is to check to see if the quadratic expression has a common factor. In this tutorial I introduce you to what a quadratic expression is and then look at factorising quadratic expressions where there is a highest common factor (HCF).
Difference of two squares
Some quadratic expressions do not have a common factor but consist of two terms separated by a minus sign and each term is the square of something. This is known as the difference of 2 squares type.
Quadratic Trinomials
Some quadratic expressions have 3 terms (trinomials) and no common factor yet can still be factorised.
There are two methods of factorising such expressions.
- by grouping
- by inspection.
Which method you choose is up to you but I generally prefer method 2 as it can be quicker but requires a bit more practice.
Method 1: Factoring Quadratic Trinomials by Grouping
In this video I show you how to factorise trinomials by grouping
Method 2: Factoring Quadratic Trinomials by Inspection (1 of 7)
In this video I show you how to factorise easy trinomials by inspection where the first term is x².
Factoring by inspection (2 of 7)
I now extend the work on factorising quadratic trinomials (3 terms) to ones where the first term is not x² only. I would encourage you to look at all the videos as the thinking changes depending on the signs in the trinomial. This is not an easy topic and requires patience.
In the first of these tutorials I show you how to factorise a trinomial with all terms positive.
Factoring by inspection (3 of 7)
In the next tutorial I show you how to factorise a trinomial where the 2nd term is negative and remind you of an important stage in the 2nd example.
Factoring by inspection (4 of 7)
In the next tutorial I show you how to factorise a trinomial where the 3rd term is negative. An important one to try.
Factoring by inspection (5 of 7)
In the next tutorial I show you how to factorise a trinomial where the last 2 terms are negative.
Factoring by inspection (6 of 7)
In the last tutorial in this section I show you how to factorise a trinomial where the x² term is not a prime number and so can be split into factors. This can often be a lot harder as there are more combinations to try.
Factorising by inspection – extension (7 of 7)
Sometimes a trinomial can be disguised as a quadratic expression. Check out the tutorial if you cannot factorise them.