Week 10 marks the first blog post while during the COVID-19 Pandemic quarantine. Most, if not all of our lessons are going to be in online classes within the confines of our homes. Personally, I find it hard adjusting to this new way of schooling, but I’ll try my best to both learn and display the knowledge gained from these classes. This blog will be covering what I learned while inside my bedroom as opposed to the classroom.

We reviewed the last topic that we were learning before spring break, which was factoring trinomials. Generally there are three steps to go through when assessing a trinomial question, and it goes like this:

Step 1: Check if there is something common within all the terms, or look for the Greatest Common Factor. If there is a common factor, divide all terms and place the GCF behind a parenthesis.

Note that ALL terms need to have a common factor in order for this step to apply, if even one term is out of line, disregard the step and go straight to the next step.

Step 2: Check if there are two terms. If there are two terms, it’s likely that it’s a Difference of Squares question. A difference of squares question is when the constants are perfect squares and the variables are even, and so we can factor by square rooting.

Two key things to note is that Difference of Squares questions –like the name suggests– need to have subtraction as its operation, if it also has a variable power that is not even or a constant/coefficient that isn’t a perfect square, then the whole step is to be disregarded and we move on to the next step.

Step 3: Check if it follows the formula: . This pattern means that its possible to turn the trinomial into two simple binomials by finding two numbers that can add into the second term while multiplying into the third term.

Sometimes however, you would go through all the steps and find that the trinomial simply can’t be factored and say its not factorable. But although some trinomials may look VERY unappealing, there is a fourth step you can do to try and factor “ugly” trinomials. One such example of an “ugly” trinomial is  which I will show how to factor.

Start off by drawing a 2×2 grid, then place the first term on the upper-left box and the third term on the lower-left box

Now, multiply both and find a factor that adds into the second term and place them into the remaining boxes.

With the grid complete you can now find the final answer. One way to find the factored answer is by looking for numbers that are in common with each other, here and 15x both have 5x in common, so you should align them together like so

In this case, in order to get  you need another x to multiply into it, and in order to get 15x you need to multiply 5x by 3, so align them by their respective boxes like so

Now there’s only one term left, and 2 is the number that can multiply into 2x and 6 from the x and 3 from earlier.Getting the one term usually helps you find the remaining terms. Our final answer is (5x+2)(x+3).

And that’s how you factor trinomials.

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