This week, we finished our polynomial unit test and learned how to solve “ugly trinomials”. These are expressions that are not are not able to be easily solved by just looking at them or using any of the four hints to factoring polynomials. In this blog post, I am going tok show you some tips and tricks to help you efficiently find the answer to these difficult expressions.

Step 1: Lets say you have an expression that looks like this

First thing first, we can see that there is a 3 to the power of 2 at the start of the expression. Draw out your two bracketed areas, place a 3x at the start of the first bracketed area and an x at the start of the second bracketed area. Example: (3x    )(x     )

Step 2: Looking at the last number of the expression, we are going to find any multiples of that particular number. In this case, the only multiples of 8 would be 1,8 and 2,4.

Step 3: This step is basically trial and error. You take each pair of numbers and try them in different orders in the blank areas within the brackets. You also need to figure out whether the numbers you are using should be negative of positive. You will know if you have chosen the right pair and placed them correctly by using the claw method to then expand the equation. if the two new numbers you get from expanding the equation equal to the middle monomial in the equation (in this case it is -2x), then you know that you have correctly solved the question.

The answer to this equation is (3x+4)(x-2)

This week we learned different methods you can use to to multiply to monomials to create a trinomial. In this blog post I am going to show you how to use the the distributive method because I find it the easiest and most efficient way to find your answer.

Let’s say you have an equation that looks like this:

(7x+9)(5x+2)

This is where you can use this method. All you have to do is multiply the different terms in a specific pattern.

This photo shows which terms need to be multiplied together, in what order (Blue 1st, red 2nd, green 3rd and black 4th).

If done correctly, your answer should look like this:

+ 14x + 45x + 18

Then you add your like terms together:

+ 59x + 18