Exercises 100–102 will help you prepare for the material covered ...

Question

Exercises 100–102 will help you prepare for the material covered in the next section.

Factor: x^2 - 6x + 9

Accepted Answer

Welcome back. I'm so glad you're here. We're given this trin Amiel expression here, H squared minus 34 H plus 289. And we are asked to factor it. Well to factor it, we can set up two sets of parentheses and we're going to look at our first term in the train oh meal H squared and we ask ourselves what times what gives us a church squared and that is going to go in the first spot in each of the two sets of parentheses. Well sometimes we've got options. You might have a lot of different things but this time it's just going to be a church times H and that's going to make the next step a lot simpler because now we can just say what times what gives us a positive 289 and What two numbers add up to a negative And that's what's going to go into those two blue spaces. Well what times what is a positive 289 but adds up to a negative number. Well, to get positive 289 you can have a positive times a positive or a negative times a negative. And to add up to be a negative number, they are going to be a negative times a negative And 289. Well that is 17 times 17 which also adds up to 34. Now if this is a little bit confusing, let me show you what we're doing, we're doing the reverse of the foil process here and we can always check by going through the foil process. F should be read. We can always check by going through the foil process to make sure that we factored correctly. So let's do that are firsts here. H. Times H. Gives us a church squared our outside terms H. Times negative 17. Give us negative 17. H. Our inside terms negative 17 times H. Again negative 17 H. In our last negative 17 times negative 17 are positive 289. We go through and we'll combine our like terms in the middle will have H squared minus 34 oops 34 H plus 289. And that matches the original Trina meal we were given. So we know we factored it correctly but none of our answer choices match H minus 17 times H minus 17. Well that's because H minus 17 times H minus 17 is the same as H minus 17 squared. We look at our answer choices and that matches with answer choice B. Well done, we'll catch you on the next one.

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