This week in Precalc 11 we learned how to factor an “ugly trinomial” which is a trinomial that has a coefficient in front of the $x^2$. This is when we can’t use our factoring 1 – one thing in common, 2 – 2 terms (difference of squares), 3 – 3 terms pattern (product & sum). Factoring a trinomial is actually kind of easy once you have figured out the way you like to solve them. There’s two ways, the first way is just guessing and plugging in numbers which can be difficult because you are guessing until you find the right number and that can take forever. The second way is to use a visual piece that’s called the box method. I personally like it better this way because it’s more straight forward and efficient. So today I will be showing how to factor an ugly trinomial using the box method correctly.

This is the ugly trinomial –

Step 1 create a square and plug in the first and last terms in the trinomial *the first term goes in the top left hand corner and the last term goes in the bottom right corner –

Step 2 fill in the empty spots in the box. Do this by multiplying the first and last terms together. Then you find the multiples of the number until you have hit the two that add or subtract to the term in the middle which in this case is our -5mn. Once you have found your two multiples then you plug in those numbers into the box *it doesn’t matter which spot you place it in so long as it’s an empty one *if the leading coefficient sign has more positives than the negatives than the bigger number in the multiples is going to be positive –

Step 3 find what’s common and there you go. You find whats common across and then up and down *whatever sign the term is on the outside is going to determine the sign of the term that’s common –

To check if you did it right just use foil and see if you get the trinomial you had to start with –

Here’s another example –