![]() So as you imagine it's nice to factor out a three first, so it's See if you can do it (laughs) now that I wrote theĪctual right thing there. Out, so it's gonna be three times x squared plus, oh whoops, this should be an x here, my apologies. So you might immediately see that all of the terms are divisible by three, so let's factor three Alright, I'm assuming you had a go at it. ![]() Practice, and like always, pause the video and see if youĬan work through it yourself. Term, and in this case it was three and negative four, we were able to factor it this way. And then we saw here, hey if we have a leading one coefficient here on the second degree term and we have it written in standard form, well let's think of two numbers that add up to this coefficient and whose product is equal to the constant So once again, at first try to factor out any common factors. Intimidating to you I encourage you to watch the videos on introduction to factoring polynomials. The first is going to be x plus, the first is going to be x plus three and then the next is going to be, we could say x plus negative four or we could say x minusįour, and we're done. So we can write inside the parentheses, so let me write, so this is gonna be four times, so we can factor ![]() You add these two together, you take their product, you clearly get negative 12 and then you add them Let's see, negative three and four would be positive one, but three and negative four works out. Two and six, negative two and six would be four, negative six and two would be negative four, One it would be negative 11, but either way that doesn't work. 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. 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. 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.
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