How to Add Polynomials

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When adding polynomials, simply add the like terms together, drawing a circle around one set of like terms, a square around another set and a triangle around a third set to easily visualize the problem. Add together polynomials with information from a standardized test prep instructor in this free video on education.

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Let's take a look at how to add polynomials. So here's an example, a polynomial might be 2 X squared plus 3 X plus 5. Another polynomial might be 3 X cubed plus 2 X squared minus X minus 7. Alright, if we want to add these two polynomials, this being a polynomial and this being a polynomial. By the way, polynomial just means many termed. Poly means many, I guess, and nomial is like term. So a polynomial's a many termed expression. And this has one, two, three terms. It's a trinomial or generally a polynomial. This one has four terms, a polynomial. When you add polynomials, all we're going to do is we're going to add like terms. That's the key. Add like terms. So you notice that I already lined them up actually so that the like terms are underneath each other. In other words, these match. These just have X, no exponent so they match. The assumed exponent when X is by itself is 1. These are both X squared, so they're like terms, and X cubed doesn't have a like term over here, so I put it by itself. And when we add them, we're just going to add the like terms. So when I add these two, I get 3 X squared. It's kind of like this plus zero. I get 4, I'm sorry, that was X cubed. This is 4 X squared. Now this is 3 X plus negative X. It's really like 3 X minus X. So that's plus 2 X. And this is positive 5 plus negative 7. It's really like five minus seven, so it's going to be negative 2. So when you add this polynomial to that polynomial, this is what we get by adding like terms. Now you don't have to write them above each other. They could have been next to each other. Could have been this plus, then you could have written it here. And in that case, all you're going to do is identify the like terms. If that's easier for you, great. If it's hard, I actually find students have a lot of luck if you say that this one is X squared, circle it, and then circle the X squared here. This one is X to the first, maybe put a box around it, put a box around this one. Now actually I messed up here. You do have to put the sign with the box or else you may forget. For example, that negative we need. And then the one by itself, you can do a triangle and a triangle. And then if the numbers were next to each other, you wouldn't know what goes with what and then you'd add the like terms and get the same answer.

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