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\nMaster How to solve a quadratic equation with two terms by factoring out the GCF\n

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\n\nPublisher:\n\nBrian McLogan\n\n\n
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\nMaster 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...\nMaster 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.

So 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.

Now, 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.

So 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.

So 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.

For 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.

However, 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.

So 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.

But 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.

So 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.

So 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.

And 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. OK?\n
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Media Length
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7:27
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Grade
12th - Higher Ed
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Subjects
Math
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Source:
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\nBrian McLogan\n\n
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Date
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2015
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English
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For Teacher Use
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Concepts

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factoring, zeros, solution set, terms, variables, solutions, roots, factoring quadratics, quadratic equations, quadratic functions, x-intercepts
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math, maths, how to, learn, help me with math, quadratic equation, quadratics, quadratic, gcf, factoring out the gcf, solving quadratic equations with two terms, solving quadratic equations with only two terms, solve, quadratic equations only two terms, how to factor quadratic equations with 2 terms, algebra, solving by factoring, solving a quadratic, द्विघात समीकरण, how to factor, square root, common multiple, product property, expressions equal, common factor, common, solution, product, factor, equal, equation, left, side, equals, divide, apply, variable, ahead, thing, make, guess, case, share, squared, check
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