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If you went the other way around, if you went negative 12 and Thinking about negative one and 12, negative one plusġ2 would be positive 11. So you could think about one and 12, and whether you're So let's think about the factors of 12, and especially think about them in terms of different sign combinations. Going to be a negative that means one of them, that means they're gonna have different signs. It's like, okay, if I have two numbers and their product is We do in other videos, and here the key is to realize that hey, maybe we can use it here.
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So are there two numbers, a plus b, that is equal to negative one and whose product is equal to negative 12? This is a technique that That add up to negative one? You didn't see a one hereīefore but it's implicit there. I've written it in standard form where I have the second degree and then if there's a first degree term, and then I have my constant term or my zero degree term, and if I have a one coefficient right over here then I say, okay, are there two numbers whose sum equals the coefficient on the first degree term, on the x term, so are there two numbers Now how would we do that? So over here the key realization is alright, I have a one as a coefficient on my second degree term. Now are we done? Well no, we can factor what we have inside the parentheses, weĬan factor this further. You can distribute the four and verify that these two expressions are the same. I just divided each of theseīy four and I factored it out.
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This would be the same thing as four times x squared minus x minus 12. Four is clearly divisible by four and 48 is also divisible by four. You might have noticed is that there is a commonįactor amongst the terms. Pause the video and try toįactor that as much as you can. Let's say I have the quadraticĤx squared minus 4x minus 48. Do all of, check whether the terms have a common factor, and if they do it never hurts to factor that out. And as we'll see, in this example, trying to factor out a common factor was all we had to do, but as we'll see in future examples, that's And that's about as much as we can actually factor, and you can verify that these two expressions are the same if you distribute the 3x,ģx times 2x is 6x squared, 3x times one is 3x, and Have a 2x left over there and then 3x divided by 3x, So if you factor out a 3x, 6x squared divided by 3x, you're gonna Both of them are divisible by three, six is divisible by three and so is three, and both of them are divisible by x, so you can factor out a 3x. So this one might jump out at you that both of these terms We have other videos on individual techniquesįor factoring quadratics, but what I would like to do in this video is get some practice figuring out which technique to use, so I'm gonna write a bunch of quadratics, and I encourage you to pause the video, try to see if you can factor that quadratic yourself before I work through it with you.