How do I factorise 3x+9

Factorise means that we want to take factor in front of the parenthesis. It means that that factor multiplied by every argument in the parenthesis will give starting value.

Lets think about 3x+9. To check what factor we can take, we have to check divisibility.

3 is divisible by 3 and 1

9 is divisible by 9, 3 and 1

Now we checking what highest number is repeated in divisible numbers. Its 3, so we can take 3 in front of parenthesis, so

3x+9=3 (1x+3) - its the result

I divided 3 by 3 and 9 by 3 to get this value

Factorising is essentially putting into a shorter, more compact form using brackets.

You need to check if the added number is divisible by 3 (found in the 3x), which 9 is. This makes it considerably easier.

Since both the coefficient and the added number are divisible by 3, you can put 3 infront of the brackets-

3 ()

You need 3x to make this true, and the coefficient of the brackets multiplies the inside.

So you only need to put one x in the brackets.

3 (x+)

This also works with the 9. (as 3x3 = 9)

3 (x+3) is your final factorisation.