factorise the equation x^2+17x+70

Firstly, you can see from the equation that each bracket must contain an x since these multiply together to give the x^2. So you get (x..)(x..)

Next, to obtain the last number of the equation you must have two factors, that multiply to give 70, in the brackets. These COULD be 1 and 70, 2 and 35, 5 and 14 or 7 and 10.

Now to get the middle part of the equation, 17x, think about the factors of 70 that may add or subtract to give 17x. You also have to think about whether or not these factors have to be positive or negative to get the desired number. In this case it is 7 and 10, so factorising the equation gives: (x+7)(x+10).

Note: attempting a few quadratic equations will allow you to 'see' almost immediately what factors are needed for the brackets and this is more ideal than writing out all of the factors