Adding and subtracting polynomials of degree two
About this video
Sal adds and subtracts two degree-two polynomials and writes each answer in standard form. He combines like terms (terms of the same degree), and when subtracting a polynomial he distributes the negative one to every term inside the parentheses.
You'll be able to
- identify like terms as terms with the same degree.
- add two polynomials by combining like terms.
- subtract a polynomial by distributing negative one to every one of its terms.
- write a polynomial in standard form, from highest degree to the constant.
Key words
- like terms
- Terms with the same variable raised to the same power (the same degree), such as 4x^2 and -8x^2.
- degree
- The power of the variable in a term; x^2 is second degree, x is first degree and a constant has degree zero.
- standard form
- A polynomial written with its highest-degree term first, then each lower degree, ending with the constant.
- constant term
- A term with no variable, just a number, like 7 or -6.
Transcript
- [Instructor] So we have two different expressions here, and what I want you to do is pause this video and see if you can rewrite each of these as a simplified polynomial in standard form. So pause the video and have a go at that. All right, now let's do this together.
So this first one, we are adding two polynomials. And I could just rewrite this as negative five x plus four x squared plus seven, and since I'm adding this entire second polynomial, I could just say this is going to be plus three x minus six minus eight x squared.
Now, the key is is we wanna combine like terms. And what do I mean by like terms? The ones that are the same degree. So for example, here I have four x squareds, and then I am subtracting eight x squareds. So if I had four of something and if I subtract eight of that same something, I am now going to have negative four of that something.
And that, in this case, that something is x squareds. Now, let's go to the first-degree terms. So I have negative five xs, and I also have three xs. So if I take three xs and I subtract five xs, well, I'm going to have negative two xs. And then last but not least, I have our constant terms.
I have a seven and I subtract six from that. I am going to be left with one. And there I have it, I've simplified it. It's a polynomial and it's in standard form. I've put the highest degree term first, the second-degree term, then the first-degree term, and then the constant term.
Let's do the same thing with this one. Now, this one, I can rewrite this first polynomial, the first part of this expression, five y plus three y squared minus nine. But we have to be a little bit careful here, because here we are subtracting this second polynomial.
Another way to think about it is, we could view, if I'm subtracting it, that's the same thing as negative one times all of this. So if I wanna remove these parentheses, I have to distribute this negative one onto every term. So negative one times eight y squared is negative eight y squared.
Negative one times negative one is positive one. Negative one times two y is negative two y. And now I can do what I just did in the previous example. I could, for example, say, all right, where are my second-degree terms? I have three y squareds, and I'm going to subtract eight y squareds from that.
Well, that's going to be, let me scroll down a little bit, that's going to be negative five y squareds. And then, I could go to my first-degree term or terms. I have five ys, and then from that, I'm going to subtract two ys. Well, that's going to give me three ys.
Plus three y. And then, last but not least, I have negative nine here, and then I'm going to add one, which would get us to negative eight. And we're done.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.