Main content

### Course: Algebra 1 (Eureka Math/EngageNY) > Unit 1

Lesson 3: Topic B: Lesson 8: Adding and subtracting polynomials- Polynomials intro
- Polynomials intro
- The parts of polynomial expressions
- Evaluating polynomials
- Simplifying polynomials
- Adding polynomials
- Add polynomials (intro)
- Subtracting polynomials
- Subtract polynomials (intro)
- Polynomial subtraction
- Adding & subtracting multiple polynomials
- Add & subtract polynomials

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Simplifying polynomials

Simplifying the polynomial 3x²-8x+7+2x³-x²+8x-3 by combining like terms. Created by Sal Khan.

## Want to join the conversation?

- at3:19when sal talks about being redundant what exactly does he mean?(26 votes)
- Redundant means repetitive (If you say the same thing over and over, you're being redundant.)

Hope that helps.(39 votes)

- Could factoring be considered a part of the simplifying process? Because all the terms at the end are divisible by 2 which could give us:

2x^3 + 2x^2 + 4

2(x^3 + x^2 + 2)(7 votes)- Yes, that would be perfectly legitimate.(8 votes)

- is there anyway i can practice this?(2 votes)
- Hi!

You are on one website that can help you right now! Khan Academy will always help you to master a problem and your teacher will be blown away that you can do it!(11 votes)

- How can you be sure that something cannot be simplified further?(4 votes)
- When you see that there no more like terms and every term is different.(8 votes)

- If a problem like this is already arranged with the highest terms to lowest terms, would my answer change if I mix the numbers around like what he did in the video? Because if so, then it becomes easier for me to understand what operation(+-) to use on each term. This probably makes no sense(3 votes)
- I don't think it matters too much, unless you're factoring. I'm pretty sure you
*can*arrange the terms any way you'd like, however, most teachers want you to put the polynomial in standard form (highest to lowest degree)(5 votes)

- 3:33Sal said that we finished simplifying the polynomial but can't we group the 2x^3 and 2x^2 as 2x^2 (x +1) ?(2 votes)
- If you were asked to simplify the polynomial, you should have a list of all unlike term like shown in the video: 2x^3 + 2x^2 + 4.

You would not change it into: 2s^2 (x + 1) +4 for 2 reasons:

1) Factored form is not simplified form.

2) Even if asked for factored form, you would not factor only 2 out of 3 terms. You would need to factor a common factor from all 3 terms.

Hope this helps.(6 votes)

- *what does sal mean when he says highest degree at1:05?*(3 votes)
- The highest degree means the highest powers among different terms of that polynomial.

Hope you understand...(2 votes)

- how do you do that with fractions(4 votes)
- weird. during some point in the video, it said x^2+x^3 can not be simplified.(2 votes)
- Aiden,

That statement is correct. You cannot add variables of different degrees.(3 votes)

- How is 3x² - x² = 2x²?? I'm a little confused because wouldn't that mean x means 1? Or... Something...? Is it because of the negative?(1 vote)
- Remember,
`x`

is the same as`1x`

. And, in this problem,`x²`

means`1x²`

When a variable does not have a coefficient (a number) in front of it, the number is always a 1.

So,`3x² - x²`

means`3x² - 1x²`

These are like terms where we add / subtract their coefficients: 3 -1 = 2

Thus,`3x² - 1x²`

=`2x²`

Hope this helps.(5 votes)

## Video transcript

simply 3x squared minus 8x plus 7 plus 2x to the third minus x squared plus eight x minus 3 so when we simplify this we're essentially going to add up like terms and just as a reminder we can only add or subtract like terms or simplify like terms and just a reminder and what I mean by that if I had an x squared to an x squared these are like terms they're both x terms raised to the same power the same degree so if I have one x squared and another x squared well then I have 2x squared - this is 2x squared If I have an x to the third - let's say I have 3x to thirds plus another 4x to the thirds Well that means I have 7x to the thirds - 7x to the thirds I can't take an x squared and add it to an x to the third I cannot simplify this in any way, so this you cannot simplify cannot simply - these are not like terms just because they both have Xs The Xs are not to - they are not to the same degree With that in mind let's look at the Xs to the same degree Let's start with the highest degree So the highest degree or the highest exponent on an x here - is actually this x to the third here but it looks like the only one it's the only place where we're raising x to the third power so that can't be merged or added or subtracted to anything else so let's just write that down. so we have 2x to the third and let's look at the x squared terms. We have 3x squared over there and we have a minus or we can view as a negative x squared over there so if we want to simplify we can add these two terms - we can add- so let me just write it down we can add 3x squared to negative x squared so I'm just rearranging it really right now I'm putting the like terms next to each other so it'll be easy to simplify now let's just worry about the x to the first terms or just the x terms you have a negative 8x term right over here so let me write it over here negative 8x and then you have a positive 8x term right over here, so let me write that down so positive 8x and then finally let's look at the constant terms you can view those as times x to the zeroth power and the constant terms are - you have a positive 7 over here - so plus 7 and then you have a negative 3 over here you have a negative 3 so all I'll I've done is I've really just used the communative property of addition to just change the order - or addition and subtraction - to change the order in which I'm doing this I've just rearranged the things so the like terms are next to each other but now we can simplify so we have 2x to the third - nothing to simplify that with but then if we subtract - if we have - let me do that in the same blue color if we have 3x squared and from that we're taking away an x squared well, we're only gonna have 2x squared left so that's gonna be plus 2x squared and then over here if we have negative 8 Xs and then we add 8 Xs to it or you can actually swap these around you could view it as you are subtracting 8 x from positive 8x we'll those are just going to cancel out so it's just going to be zero - I could just write plus zero here, but that'd just be redundant it wouldn't change the value and then finally I have a plus 7 minus 3 well that is just clearly 7 minus 3 is 4 so I have plus 4 And we're done! We've simplified it! 2x to the third plus 2 x squared plus 4