Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero

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  • 0:02 Solving Quadratics
  • 1:14 Greatest Common Factor
  • 2:36 Multiplication…
  • 3:28 Another Example
  • 4:09 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When it comes to solving quadratics, we have at our disposal several methods. Watch this video lesson to learn one such method you can use to solve quadratics that don't have a constant term.

Solving Quadratics

To solve a quadratic means to find the value of our variable for which the quadratic equals 0. This is easy to remember if our variable is x, which in most cases it is. When x is our variable, we can think of a treasure map where we are looking for the spot where the x is so we can find our treasure.

Recall that the general form of a quadratic is ax^2 + bx + c = 0, where a, b, and c are numbers and a cannot be 0. When we set this equation equal to 0 and solve for our variable x, we are solving it or finding out the location of our treasure.

There are many methods out there that we can use to solve these types of equations. In this video lesson, we will learn one such method that we can use when our c value equals 0.

The method that we are about to learn will work for quadratics such as x^2 + x = 0, but not for quadratics such as x^2 + 2x + 1 = 0. This method only works for those quadratics without that last constant term, the term that is just the number.

The Greatest Common Factor

Now that we know what kinds of quadratics we'll be working with, let's take a look at an example to see how this method works. The method we are going to use involves finding our greatest common factor first. So, if you feel a bit rusty in this department, take a moment to pause this video to refresh your skills in finding the greatest common factor, the largest term that divides evenly into all the terms.

Let's see how we do this by solving our quadratic x^2 + x = 0. We see that this quadratic does not have a constant term, so we are okay in using this method. So now, we start by finding our greatest common factor.

We look at our first term, our x^2, and our second term, our x. We look for what they have in common. That gives us a clue as to what the greatest common factor is. We see that they both have an x in common. Do they have anything else in common? No, so that tells us that the x is our greatest common factor. We see that we can also divide both terms equally by our x.

Once we have found our greatest common factor, we factor our quadratic using it. If you need to refresh your factoring skills, feel free to pause this video again while you go ahead and do that. So, factoring out our x, we will get x(x + 1) = 0.

The Multiplication Property of Zero

At this point, we apply the multiplication property of zero to help us solve our quadratic. The multiplication property of zero tells us that anything multiplied by zero will equal zero. So, that tells us that if either of our factors equals 0, then that will be an answer.

So to find what our x equals, we can set both of our factors, our x and x + 1, equal to 0 to solve for our x to find our answers. So, we get x = 0 and x + 1 = 0.

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