This week in Math 10 we learned how to factor trinomials that have a coefficient that isn’t one in the first term. There are two methods to factor these but I’m just going to explain one, the area model. I like this method better because it gives me more of a straight answer instead of a “guess and check” answer. In this example we’re factoring 12x^2 – 8x +1. The first step is to draw a box and separate it into four sections. In the top left box we write the first term and in the bottom right box (diagonal the first term) we write the last term. Now on the outside of our boxes we write the first term multiplied by the last term, so in this case it’s 12x^2. Then below that we put the middle term (-8x) so we know which numbers we’re working with. The next step is to find 2 numbers that multiply to get 12x^2 and add to get -8x. We end up with -2x and -6x and we put them in the blank boxes and it doesn’t matter which one goes where. Now we find the common factors by going across and down. So we have to find the common factors of 12x^2 and -2x (which is 2x), -6x and 1 (which is 1), 12x^2 and -6x (which is 6x) and -2x and 1 (which is -1). So the next step is to put these answers in brackets so we end up with our answer which is (6x – 1)(2x – 1). Remember to put the number in the brackets in descending order according to degree of the exponents!