How to Solve Roots of Polynomials

Series Summary

Teachers play an integral role in the development and education of children. Working in schools, academies or a community setting, a teacher's job focuses on facilitating student learning through lessons and demonstrations. High school teachers, in particular, play an important role in helping prepare students for college and jobs in the real world. All teachers face the difficult job of keeping students engaged and excited about learning. While education careers are quite difficult, for most teachers the benefit of shaping young minds far outweighs the challenges. In this free video series on education, a standardized test prep instructor offers information on common English and math problems. Find out how to cite sources in APA style and how to use a comma in dates. Learn about solving roots of polynomials, learning algebra, and discover the steps to finding a prime number. Improve math and English skills with tips from these free video lessons.

Video Transcript

"Let's talk about how to get the roots of a Polynomial. Essentially, what that means is, is that we have something. We have a Polynomial. And we want to know what values are going to make this, what values for the variable. X in this case. Are going to make the Polynomial work. We're solving it. Roots by the way, is a synonym for the word, solution. Or zero. Those are the words we use in algebra for root. They all mean the same thing. So if we have it factored. As we do here. The way we get the roots are. We're going to look at each part. And we're going to say, when you have this times this times this, equals zero. In order to multiply to get zero. One of these guys has to equal zero. In fact, if any of these was zero. Doesn't matter what happens in the other parenthesis. Anything times zero is zero. So we're going to say hey, what would make this guy equal zero. And the answer is zero. So X could equal zero. Now we say, what would make this equal zero. So you're just going to rewrite it. Equal to zero. Solve, add three to both sides. X equals three. So there's another root or solution for zero. O.k., what would make this thing zero. 2X plus 4 equals zero. Solve it. Divide by two. Negative 4 divide by 2 is negative 2. There's another solution. And lastly, this one. X plus five equals zero. I'm writing X plus five equals zero. Because I'm saying, what would make this expression in the parenthesis, equal to zero. So I'm going to subtract five from both sides. X equals negative five. That's our last solution. So there are one, two, three, four solutions. To this Polynomial. either zero, three, negative two or negative five. Will make this work. And that's because one last time. If you plug in three for example. 3 minus 3 is zero. So this expression will equal zero. Doesn't matter what these guys are going to wind up equally. Because zero times anything is zero."