Factorise 3x^2 + 15x

To factorise an equation you need to look for factors that all the elements of the equation (3x^2 and 15x) have in common. You can do this all at one or in steps, to start with you can see that both parts have x as a factor, this means you can rewrite the equation as x*(...), to find what is in the brackets you need to divide the original equation by x, which is: 3x + 15. Therefore you can write 3x^2 + 15x as x*(3x +15) instead (a partially factorised version). However this is not fully factorised as you can see the two elements still have a common factor of 3. Doing the same as before with the x, the original equation can be writen in a fully factorised form: 3x*(x+5). You can see that it is not possible to factorise it further as the elements within the brackets have no more common factors.