Factoring polynomials

This week in math 10 we learned how to deal with factoring the “ugly” polynomials. For the most part, the “ugly” polynomials are trail and error, which means that you just have to do it until you get it right. This method is good to use, but it will get harder once a larger coefficient and more variables get added. There’s no need to worry once it becomes more complicated we were taught the box method which happens to help a lot.

 

The polynomial used as an example is an “ugly” trinomial, and the reason why is because it cannot be factored using the $latex/ x^2$ method or the perfect square method.

Box method – First, you’ll need to draw a square with 4 sections. You’ll then place the first term on the top of the left side sections and place the last term on the bottom of the right side corner, you should have 2 open spaces. At this point, the first term of the equation and the last part are dealt with which means the only term left is the middle term. In order to find the missing numbers/variables that should fill in the 2 sections, you’ll multiply the first and last coefficient. When you get the answer you’re going to need to find 2 numbers that add up to the middle term but at the same time multiply to the answer given. You then will have 2 integers that you’ll then place them with the variable to fill in the missing section. The final step you’ll need to do is factoring and make your 2 brackets and place the results in them.