This week, we learnt how to factor “ugly” trinomials. An ugly trinomial is a trinomial that has a number before the first variable (ex: ). The method that I use is a box.

We’re going to use the equation

1. Your first step is to draw a box and divide it into four parts. Next, you put the in the top left part of the box and the +4 in the bottom right part of the box.

2. Now, you multiply by +4 which equals now, you find the factors of 12. They are:

3. Next, you figure out which of the factors when added together make 8. 1+12=13 so that one can’t be the answer. 3+4=7 so that also isn’t the right one. That means the only possible answer left is 2+6. 2+6=8 so it’s the right one. If the +4 was actually a -4, you would look to see which factors subtract to the number in the middle of the equation. 8 could not be the middle number in that case however. The number could either be 11, 4 or 1.

4. Now, 2x+6x+8x so we put the 2x in either one of the parts of the box still available and the 6x in the other one.

5. Next, we find the common factors in all the numbers. In my example, I put the 6x next to the . The common factor of the two is 3x. Write that down beside the box. The common factor of 2x and +4 is +2. The common factor of and 2x is x and finally, the common factor of 6x and +4 is +2. Finally, you put all the factors that you just found together to make the factored equation which is (x+2)(3x+2).