# Factorising and Completing the Square

### Greatest Common Factor

### Video

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.

### Notes

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

A pdf of this document can be downloaded here.

### Interactive Exercises

Try the following NUMBAS exercises to test your factorising skills.

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

### Factorising Quadratic Expressions

### Videos

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.

### Notes

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.

### Interactive Exercises

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

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

### Completing the Square

### Videos

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.

### Notes

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

A pdf of this document can be downloaded here.

### Interactive Exercises

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

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

### Factorising Cubic Polynomials

### Videos

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.

### Notes

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.

### Polynomial Division

### Videos

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.

### Notes

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

A pdf of this document can be downloaded here.