This week in math we learned how to deal with ugly trinomials.  We refer to them as ugly because they are harder to factor.  An easy trinomial is very simple to factor, ugly trinomials involve multiple steps. First, what does an ugly trinomial look like compared to an easy one?

Let’s look at the differences. It’s important to know what type of trinomial it is. When factoring an easy trinomial there is an invisible one as a coefficient beside X squared. Otherwise, in ugly trinomials, their first term can have a coefficient greater than one or as well as an exponent greater than two.

When solving ugly trinomials we have to use a diagram to help us. First, we take the first and last terms and place them in the first and last boxes in the square we have drawn.  Next, we have to find out what two numbers belong in the extra boxes. So, we multiply the first and last terms together to get a number that will help determine what we are looking for.  Then we have to find two numbers that multiply, in this case, to 14 and subtract to -5 (the middle term).  To find these two numbers we have to factor 14.  Make sure you pay attention to the middle term and if it is negative or positive.  If the middle term is positive then the greater number will be positive, otherwise, if the middle term is negative the greater number will be negative.

Finally, we place the two numbers that add/subtract to -5 and multiply to 14 in the empty squares. After this, we add a variable to these numbers, in this case, P. moving from right to left we have to pull out the GCF of the pairs. After, you do the exact same thing top to bottom.  Make sure you acknowledge if it is a negative or positive GCF. When you end with four numbers and two pairs you just found what makes up that ugly trinomial.