Log inSign up for FREE
Library

Guided Lesson: Factorising Quadratic Expressions

Last updated over 2 years ago
19 questions
In this lesson, you will learn how to factorise quadratic expressions by 'splitting the middle term'.
This can be applied to forms of quadratic equations where the constant term is not a perfect square
eg.


This factors into the form:




or when the x^2 term has a coefficient
eg.


This often factors into the form:

To apply this method, you must first find two numbers a and b such that the sum of the numbers gives you the coefficient of the middle term and the product gives you the product of the coefficients of the first and last term.
Is that sentence freaking you out yet? Let's break it down!

This is a quadratic expression


You need to find 2 numbers, a and b so that:

a+b = 9 and
a*b = 14*1
1

What are your two numbers?
(Write your numbers in this form a, b)

Now, you split the middle term using the two numbers you found, like so:


Then, we will split the expression into two parts.



What is common in both terms in the 1st bracket?

And what is common in both terms in the second bracket?

You take out what is common outside the bracket on both terms.
1

What is common in both terms in the 1st bracket?

1

And what is common in both terms in the second bracket?

1

What expression do you get when you take out the common variables out of both brackets?

1

What do you observe within both brackets? Anything interesting?

You will have got an expression like this:


Now you have two terms, what is common in both terms?

We will take out what is common in both terms and put the remaining in another bracket. What you get now is the final answer
1

What is common in both terms?

1

Enter your final answer

Watch this video if you need a refresher!
1
1
1
1
1
1
1
1
1
1
1

For what values of b is the expression factorable?

1

Name four values of b which make the expression factorable: