Adding & subtracting polynomials
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Adding polynomials (old)
Add, and they give us 5x squared plus 8x minus 3 plus 2x squared minus 7x plus 13x. So we can really view this as just adding two polynomials. And actually, the second polynomial here can be simplified right off the bat. We have two like terms here. It's not the 2x squared. There's no other 2x squared term in this polynomial. But you have a negative 7x term. And then you have a plus 13x. So we could actually add these two terms. What is the negative 7 of something plus 13 of that something? Or another way to view it, what's 13x minus 7x? 13 of something minus 7 of that something? Well, that's just going to be 6 of that something. So that is just going to be 6x. And then you have your 2x squared. And you have your 2x squared right over here. Let me write it. So 2x squared. So this polynomial right over here simplifies to 2x squared plus 6x. And then we want to add it to this polynomial right over here. And what we can do is, what I like to do is just rewrite this polynomial under this polynomial. And I'm going to align the similar terms or the like terms, the terms that have the same variable raised to the same power. So we have x raised to the second power. So let's put the 5x squared over here. We have an x raised to the first power. We have an x raised to the first power. So let's put the 8x over here. And then we don't have a constant term in this yellow polynomial. We don't have anything raised to the zeroth power, any constant terms. We do here. So let's just put a minus 3. And then we could add these two things up. We have 2x squared plus 5x squared. That is 2 of something plus 5 of something is 7 of that something. So it's going to be 7x squared. And then to that, if I 6 of something and I add 8 of that something to it, well, I'm going to have 14 of that something. If I have 6x's and I give you 8 more x's, you're going to 14x's. And then we have nothing here. And so if we just add nothing to negative 3, you're just going to get a negative 3. So this simplifies to, or when we added these two polynomials, we get 7x squared plus 14x minus 3.