#### notes

We begin with a simple example: Factorise 2x + 4.

We shall write each term as a product of irreducible factors;

`2x = 2 × x `

4 = 2 × 2

Hence `2x + 4 = (2 × x) + (2 × 2)`

The factor 2 is common to both the terms.

Observe, by distributive law

`2 × (x + 2) = (2 × x) + (2 × 2)`

Therefore, we can write

`2x + 4 = 2 × (x + 2) = 2 (x + 2) `

Thus, the expression 2x + 4 is the same as 2 (x + 2). Now we can read off its factors: they are 2 and (x + 2). These factors are irreducible.