Factorising and Completing the Square

This video from Maynooth University explains how to factorise expressions by identifying the greatest common factor.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

These notes from MathCentre explain how to use the greatest common factor to factorise expressions.

A pdf of this document can be downloaded here.

Try the following NUMBAS exercises to test your factorising skills.

Please click here to view this NUMBAS question in another window.

These two videos from Maynooth University show how to factorise quadratic expressions.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

These notes from MathCentre are a resource for factorising quadratic expressions. Try the exercises on page 2 for some practice factorising quadratic expressions.

A pdf of this document can be downloaded here.

Try the following NUMBAS exercises to practise solving quadratic equations by factorising.

Please click here to view this NUMBAS question in another window.

These two videos from Maynooth University show how to complete the square for 2 different types of quadratic expressions.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

Read these notes from MathCentre to learn more about completing the square.

A pdf of this document can be downloaded here.

Try the following NUMBAS exercises to get some practice completing the square.

Please click here to view this NUMBAS question in another window.

These two videos from Maynooth University explain how to factorise cubic expressions. Note that the second video shows how long division can be used to factorise a cubic polynomial.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

The following notes from MathCentre are a resource for cubic polynomials and cubic equations.

• Introduction to cubic expressions and roots (Pages 1-4).
• How to solve cubic equations (Pages 5-9). Note: a particular type of procedure called "synthetic division" is used here. Alternatively, you can use "polynomial division", which is explained here.
• Using graphs to solve cubic equations (Page 10).

Try the exercises in the notes to test your knowledge of solving cubic equations.

A pdf of this document can be downloaded here.

This video from Maynooth University explains the method of polynomial division to factorise a cubic polynomial.

Note: All Maynooth University content is available for free at msc.maths.nuim.ie.

Pages 3-6 of these notes from MathCentre explain the technique of polynomial division.

A pdf of this document can be downloaded here.