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Factoring: Special Cases Part I - Problem 3
This problem looks like it’s kind of just annoying it's not going to help you much but actually problems like this are going to become really useful when you start doing what's called completing the square. It’s kind of what we are doing here.
They are asking me to find the missing term of this perfect square trinomial. Now we haven't really seen problems like this before so one thing I thought about doing was writing down what I know about perfect square trinomials. I know a perfect square trinomial looks like this. It’s a binomial times itself and then the product when you Foil it all out it looks like this.
Notice that I used the subtraction version a take away b because I had a minus sign in my original problem. You also know that those could be pluses. But now in our case we are going to use minuses. Okay so this is what a perfect square trinomial looks like it’s this whole piece. What I’m going to do is use this statement that uses numbers and try to translate it into this formula that only uses letters.
For example this piece the 9x² has to be something times itself. What times itself gives you 9x²? It has to be 3x, that's going to be my a piece because 3x times 3x is 9x². Then let's look at this last term 25. 25 represents my b value times itself, so b has to be 5. Once I know that I can find this piece here the product 2ab. 2ab is going to be 2 times my a value times my b value when I do that out I’ll get 30x.
So I think I’m done I think this is the right answer I think 30x is the missing term there but let's go back and Foil and make sure we got that correct. What I want to do is make sure that a take away b² in my case 3x take away 5 times itself when I Foil I hope I get that answer so let's try Foiling to check first outers inners last gives me 9x² take away 15x take away 15 more x plus 25, good when I combine those I do get -30x. That's how I know I did it right.
So a lot of times in Math you'll see problems and you don't really know where to start. If you don't know where to start one place you can begin is by writing down the definition. Write down anything you know about what's going in the problem.
All I knew is that a perfect square trinomial meant this formula and that's how I was able to begin this problem. So although it’s kind of difficult it really is valuable for you to start learning vocabulary in terms of their words and also their symbol definitions.