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What is a zero when discussing functions? Get math help for your college algebra or developmental math class with this short tutorial video that will give you the necessary steps to finding the real zeros of a function, taught by Ivette Chuca, a Professor at El Paso Community College.

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Have you ever heard the term zeroes when discussing functions? What exactly is a zero? A real zero of a polynomial function is a real number c such that f of c is equal to zero. This means when we input the real number c into the function, the output is zero. Graphically, the real zero of a polynomial function corresponds to the x intercepts. As we can see on this graph, the x intercept has a y coordinate of zero. So how do we find the zeroes without the graph? To find the zeroes algebraically, we want to find input values that result in the output value of zero. Therefore, we set the function equal to zero and solve. Let's try an example. Find the real zeroes of the function f of x equals x cubed plus 2x squared. First, we set the function equal to zero. Then we try to factor. Remember not all polynomials will be factorable. However, we have other strategies to help us find the zeroes. In this example, we will focus on factoring. We can factor out and [inaudible], which is the greatest common factor, giving us x squared times x plus 2. Now we can set each factor equal to zero. So we get x squared equals zero and x plus 2 equals zero. Next, we solve for x. X squared equal to zero, we can take the square root on both sides so we end up with x equals zero. Where x plus 2 equal to zero, we can subtract 2 on both sides, giving us x equals negative 2. These are real zeros of a polynomial function. Here's the graph. As we can see, our zeroes are represented with the x intercepts at x equals zero and x equals negative 2.