{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Master How to solve a quadratic equation with two terms by factoring out the GCF' data-url='/boclips/videos/6367368f24a5c53148750bee' data-video-url='/boclips/videos/6367368f24a5c53148750bee' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nMaster How to solve a quadratic equation with two terms by factoring out the GCF\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30355462\" href=\"/search?publisher_ids%5B%5D=30355462\"\u003eBrian McLogan\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eMaster How to solve a quadratic equation with two terms by factoring out the GCF So what I'd like to do is show you how to solve a quadratic equation by factoring out the GCF. So basically, in this one, when factoring out the GCF, what...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eMaster How to solve a quadratic equation with two terms by factoring out the GCF So what I'd like to do is show you how to solve a quadratic equation by factoring out the GCF. So basically, in this one, when factoring out the GCF, what we're looking into is looking for what is a common factor between our two terms. then we're going to divide that out, apply the zero product property, and then solve.\u003cbr/\u003e\u003cbr/\u003eSo remember, when we're looking into solving quadratics, one of the major important things, when we have two variables, we just can't simply isolate the variable. We have to go ahead and factor to rewrite the equation as a product of two quantities equal to 0. So the first thing we want to do is make sure that our equation is set equal to 0. So you can see, when we have examples of it not equaling 0-- I guess that's my only one-- when we have it not equal to 0, we want to make sure we get all the terms on the same side set equal to 0. So in this case, we have that.\u003cbr/\u003e\u003cbr/\u003eNow, the next thing we want to do is factor out its common terms. So you can see, between x squared and x, what do they share in common? What can we divide out that's exactly the same out of both of them? Well, you can see you can divide an x into an x squared, right? And you can divide an x into x. So therefore, x is my common factor.\u003cbr/\u003e\u003cbr/\u003eSo when I dived out an x, I'm left with x plus 1. And you can always check your answer. When factoring out the GCF, or factoring just in general, when you rewrite an expression as a product, you can always check your answer by multiplying it back out. x times x is x squared. X times 1 is x. So it works.\u003cbr/\u003e\u003cbr/\u003eSo now, I have the product of two expressions equal to 0. So therefore, by applying the zero product property, I can set them both equal to 0 to solve. Well, I have x is equal to 0. That's done. And then I subtract 1 here, and I have x is equal to negative 1. So therefore, my solution set for this one is 0 negative 1. Done. Oops that needs an x. OK.\u003cbr/\u003e\u003cbr/\u003eFor the next example here, I have x squared minus 56x equals 0. And again, we look at this. We have a number, and so we say, all right, what can we factor out? However, this has a number of 1. So the common factor is 1, right? 1 and 56, the only number that divides into 1 and 56 is 1. So factoring out a 1 is really not going to help us.\u003cbr/\u003e\u003cbr/\u003eHowever, we both understand that they have an x, an x squared, and an x. So therefore, I can factor out an x. So if I factor out an x in this case, I'm now left with an x minus 56. Again, x times x is x squared. X times negative 56 is a negative 56x. Now, again, I set both expressions equal to 0, using the zero product property. And then I can just simply go ahead and solve this. So therefore, I have x equals 56. OK.\u003cbr/\u003e\u003cbr/\u003eSo now, the next case, now both of my terms have a coefficient. One has a coefficient of 2. The other one has a coefficient of 4. So we want to look at, again, what is the common factor? We know they have x squared and x. And actually, for all these problems, you can see they all have x squared and x. So we know x is going to be a common factor.\u003cbr/\u003e\u003cbr/\u003eBut we're also looking for is what about the numbers? What is the common factor? What divides into 2 as well as divides into 4? Well, that's 2. So now, I'm going to factor out a 2x. When factoring out a 2x, I'm left with an x plus 2 equals 0.\u003cbr/\u003e\u003cbr/\u003eSo now, I again set these both equal to 0. So I'll have 2x equal to 0 and x plus 2 equals 0. Well, here, I can divide by 2, and I get x equals 0. Here, I subtract 2, and I get x equals negative 2. I didn't write these as in a solution set, but I guess I could do that. OK.\u003cbr/\u003e\u003cbr/\u003eSo now, let's go and get into this one. This one, you might say, oh, it looks a little bit confusing here. Now the 0's on the left-hand side. It doesn't matter. It's just another way to rewrite it. Again, we want to look at the common factor. So we look at 16 and negative 4. We know that they're going to both have common x. We can factor out the x.\u003cbr/\u003e\u003cbr/\u003eAnd then you look at 16 and 4. And you can say, all right, well, 4 divides into both of those. So that's going to be my common factor. It will be 4x. So 0 equals 4x, which is going to leave me with a 4x minus 1. 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