This week in Math 10 we finished up our polynomials and factoring unit. In this blog post I am going to explain the third part of factoring 1-2-3, factoring trinomials! I will explain how to do it and then show an example.
There are different ways to approach factoring trinomials but I am going to show the method that works best for me and what I like to do.
Step 1: The first thing I do when I get my question, is write P and S that stand for product and sum. Because I know whatever multiples to equal my product must add to equal my sum. So writing it out can help you see the problem and get the result quicker I find.
Step 2: The next thing I do is figure the two number that are going to work. It can help to write out a list of what multiplies to give you a product of 10. I can easily identify that 5 and 2 will give me a product fo 10 and sum of 7. But my problem here is that my sum is a negative number. So here I am going to use the multiplication laws that tell me if I have two negatives when multiplied together they must give me a positive answer. And by doing this I will end up with an answer of +10 and -7.
Step 3: When factoring a trinomial the answer is always going to be in two brackets. Because I see I have a squared, I am going to put a in both and the brackets. And my last step is very easy, you put -5 in one bracket and -2 in the other.
Step 4: You don’t have to do this step but you can always take your factored question and solve it to make sure you factored correctly.
Those are the simple steps to factoring a trinomial. I am going to solve another one following the same steps I showed above.
Those are the simple steps to solving a trinomial. I find with practice you don’t even need to write out the product and sum but at the start it really helped me.
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