Factor each trinomial, if possible. See Examples 3 and 4. 9m^2 -1...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 9m^2 -12m+4

Accepted Answer

Welcome back. I am so glad you're here. We are given the polynomial 49 U squared minus 56 U plus 16 and were asked to factor it. Well, first, we look at them and ask if there's anything that these three terms have in common that we could factor out in front. And I am not seeing anything that 49 negative 56 16 have in common. So next, we would look at the first term and ask ourselves what times what gives us 49 U squared. But in this case, we notice that there are a lot of squares there, 49 is seven squared and then you squared is U squared. We could rewrite that as parentheses seven U and parentheses squared. And noting that for a second, looking at the last term here, we noticed there are a lot of squares there too. Well, not a lot, just one, it's four squared. So we've got two squared. So this might fulfill the condition where we have X squared. And then we've got a minus two XY plus Y squared. If that's the case, we can set that equal to parentheses X minus Y squared and we'll have it factored just like that. So let's see if we do have a minus two XY in the middle. So what's R X R X is the first thing being squared? So X is this seven? You what's Ry? Ry is the last thing being squared here are Y is equal to four. So our two X Y will be two times X is seven, you and Ry is four, Well, two times four, Excuse ME, two times 7 times four is 56. Bring down the U. So we have a 56. You there. Yes, we do have a minus two XY with our minus 56. You so we can factor this by putting X minus Y in parentheses and squaring it. So our X again is seven U minus R Y which is four and here is our polynomial fully factored. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

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Factor each trinomial, if possible. See Examples 3 and 4. 9m^2 -12m+4