Factorise: 3x^2 - 9x - 30

The first think you can do is look to see if all of your terms can be divided by a common factor. In this case it is 3, leaving you with 3(x^2 - 3x - 10). This can be factorised further to produce something of the format 3(x )(x). The sign before the 10 is a minus, which means that the signs in the brackets will be different: 3(x-)(x+). The missing numbers must be one positive and one negative number which multiply to make -10 and add to make -3. The only options are -5 and 2, therefore 3x^2 - 9x - 30 = 3(x-5)(x+2).