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Course: Algebra (all content) > Unit 10
Lesson 2: Adding & subtracting polynomials- Adding polynomials
- Add polynomials (intro)
- Subtracting polynomials
- Subtract polynomials (intro)
- Polynomial subtraction
- Adding & subtracting multiple polynomials
- Add & subtract polynomials
- Adding polynomials (old)
- Adding and subtracting polynomials review
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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.
Want to join the conversation?
- What is a polynomial? I never learned this before.(4 votes)
- Ryan,
Here is a video on terms, coefficients and exponents of polynomials that may helps you understand what a polynomial is.
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/polynomial_basics/v/terms-coefficients-and-exponents-in-a-polynomial
I hope that helps.(13 votes)
- When Sal simplifies -7x+ 13x into 2x^2+6x at0:50, why does he add a plus sign inbetween 2x^2 and 6x? Doesn't it default to multiplication when there are no signs between numbers?(1 vote)
- It is because 6x is positive 6x, and the sign for positive is +.
Therefore, it wouldnt be multiplication(3 votes)
- How do you find perimeter with polynomials?(1 vote)
- just as moom said,a polynomial is a very broad term,it is used in almost any kind of mathematical calculation where one or more values are unknown,according to your question,you have seen that different perimeters have different "formulas",well most those formulas are polynomials.example-perimeter of a rectangle 2(l+b),it's a polynomial.in a more general sense,suppose you got 5 boxes of apples and 3 boxes of mangoes delivered to you and you don't know how many apples or mangoes are there in the boxes but you do know that the number of apples in all apple boxes are same and the number of mangoes in all mango boxes are same,so you can call the amount of mangoes in each box as 'm' and the amount of apples in each box as 'a',so now how many total fruits did you receive,well 5a+3m,that's a polynomial :D !(1 vote)
- When Sal does '2x^2 - 7x + 13x' why does he write 2x^2 + 6x instead of 2x^2 - 6x? Isn't it supposed to be subtraction instead of addition?(1 vote)
- The reason why it's +6x instead of -6x is because (ignore 2x^2 for now) -7x + 13x is the same thing as 13x - 7x, they're just rearranged (remember individual terms keep their signs, positive or negative). And so 13 - 7 = + 6, and 13x - 7x = +6x.
2x^2 - 7x + 13x == 2x^2 + 13x - 7x == 2x^2 + 6x
The thing that helps me remember the rules for adding or subtracting terms is not to think of them as adding or subtracting, but that you're just "combining" them, and whether you add or subtract depends on whether the terms are positive or negative.(2 votes)
- what is the difference between something like 5x-5-4x+3 and (5x-5) - (4x+3)?(1 vote)
- How would I do a problem with 3n4(1 vote)
- When is the box method used in polynomials?(1 vote)
- In this video he does the vertical method does anyone know if there's a video showing horizontal method?(1 vote)
- sooooo, if we have 6x^3+24x^3-70x^2=30x^3-70x^2, right?(1 vote)
- So is this just simplifying ?(1 vote)
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.