Factoring: Beyond the basics

Prime Factors

Spot a square number or a cube number using prime factors

The prime factors of 144 are: 2\times 2 \times 2 \times 2 \times 3 \times 3

These factors can be grouped as: (2\times 2\times 3) \times (2 \times 2 \times 3)

In other words: (2 \times 2 \times 3)^2

Which confirms that 144 is a square number.

Your turn – use prime factors to create a square number. Check it out using the \sqrt key on your calculator!

Extend the principle to cube numbers!

Multiplying Polynomials

Multiply any degree by any degree Expanding brackets for polynomials in general

Multiply several brackets Expanding brackets more than two

Kuta software worksheet: Multiplying polynomials (see page 2)

Problem Solving

Geometry problems – what do you notice? Geometry Problems with Quadratic Expressions notice

Geometry problems – questions attached Geometry Problems with Quadratic Expressions


Spot a trinomial that is a perfect square


For example:




These perfect squares factor as follows:




Choose your own values of a, b, and create some of your own.

Spot a trinomial that is the difference of two squares

Any trinomial of the form:


is called the difference of two squares. You can confirm that it factors as:


For example:




These differences of two squares factor as follows:




Kuta Software worksheet: special cases

Factor a trinomial where a\ne 1. Read the link to find the various approaches to a trinomial of the form:


Kuta Software worksheet: Trinomial with leading coefficient not 1

Two more:

sum of two cubes


difference of two cubes