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# More on Factorisation

We shall now factorise , where the coefficient of is not one. For example:

We shall find two numbers whose sum should be b and whose products should be ac. Once found, we break the middle term bx into the sum of these two numbers and factorise the resulting expression.

Consider , we shall find two numbers:

• Sum
• Product

These two numbers are 6 and -1

We now rewrite as as

Now, , which is .

Even if we took , we shall have , which again factorises into , as before.

Let’s look at some examples.

## Example

Factorise

We need two numbers.

Sum , product

These are 9 and 8.

So, we break x into , to obtain:

## Example

Factorise

Sum , product

Since and , we have:

Factorise

Factorise

Factorise

## Example

Factorise

Sum , product

Since and , we have:

Factorise

Factorise

## Example

Factorise

We look for two numbers with a sum of -22 and a product of 8\times15 = 120.

With trial and error, we find -10 and -12. So, we have:

Factorise