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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:   ## Example

Factorise    ## Example

Factorise    ## Example

Factorise     ## Example

Factorise Sum , product Since and , we have:   ## Example

Factorise    ## Example    ## Example

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:   ## Example

Factorise    