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# Adding polynomials (old)

An old video where Sal adds (5x²+8x-3) + (2x² - 7x + 13x). Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

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.