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## College Algebra

# Adding polynomials

Sal simplifies (5x² + 8x - 3) + (2x² - 7x + 13x). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- At0:20, Sal says that you can get rid of the parentheses. According to PEMDAS don't you have to complete everything inside of the parentheses before you move on? Why is it okay to ignore the parentheses?(8 votes)
- I'm pretty sure that this only applies if the polynomials inside the parentheses are not in simplest form. If they are in simplest form, then you can remove the parentheses. At least, that's how I do it.(5 votes)

- I don't get why -5t - 3t equals -8t on my textbook, if the subtraction sign also applies to 3t as a negative sign, wouldn't the answer be -2t because you have to change the subtrahend every time, -3t turns into 3t, then you subtract, it becomes -2t. I don't really get it.(3 votes)
- That only applies if you are subtracting a negative number. So if the textbook said -5t - - 3t, you would be absolutely right.

The best way to look at it would be as -5t + -3t = -8t.(28 votes)

- Why do you have to distribute a negative?(4 votes)
- Good question. If you have -4 -3 and you want to factor out a negative one, you would write -1(4+3). Think of the negative sign and the parenthesis as a negative one.(15 votes)

- how would you combine the terms if they had different exponents(5 votes)
- In that case, you wouldn't be able to combine the terms. Could you give me an example so that I could walk you through it? Some scenarios will allow you to add different exponents (after distribution)(7 votes)

- Why didn't he add the exponents when he added 5x squared + 2x squared?(2 votes)
- because 5x squared is (x*x)+(x*x)+(x*x)+(x*x)+(x*x) and 2x squared is (x*x)+(x*x)

when you add it together you get (x*x)+(x*x)+(x*x)+(x*x)+(x*x)+(x*x)+(x*x) the exponent never changes because you are just adding them together. this is why when combining like terms you cnt combine 3x^2 with 3x^3 when they are being added(10 votes)

- Is the process the same when you are subtracting?(4 votes)
- Yes. You follow the same process, but flip the sign of each term in the polynomial that you are subtracting. Then you add like normal.(6 votes)

- me looking at these questions that were commented years ago and the nostalgia comes of doing khan academy(5 votes)
- Add the polynomial functions: \large f\left(x\right)=4x^2+3x-5

and \large g\left(x\right)=2x^2-x+1.

Combine the like terms and type in your answer in equation form by clicking on the "Insert Content" with an arrow and select "Equation".(3 votes)- You should keep it neater, so get rid of the coding type text. just have f(x) = 4x^2 + 3x - 5 and g(x) = 2x^2 - x + 1

Since you are adding the polynomials you have 4x^2 + 3x - 5 + 2x^2 - x + 1.

To add them you do exactly as the instructions say, combine like terms. This just means look for matching variables. For instance 5x^4 - 6x^4 would be like terms since they have x^4. Combining like terms just means to do what the math says to the coefficients. so 5x^4 - 6x^4 means take 5 - 6 since the two are being subtracted. so 5x^4 - 6x^4 = -1x^4 or just -x^4

The three kinds of terms are those that have x^2, x and no variable at all. I will get you started, the non variable terms are -5 and + 1 so combining the gets you -4. can you take it from there?

I will give a different example to further help.

x^4 - 7x^3 + 3 - 5x^4 + 8x^3 + 3

here are the like terms

x^4 - 5x^4 = -4x^4

-7x^3 +8x^3 = x^3

3 + 3 = 6

So now you have -4x^4 + x^3 + 6

Let me know if yous till don't understand(4 votes)

- so in my assignment I have (x^6+9x^4-4x^2-x)+(3x^4+2x^5+3) But as you can see I have 2 more number with X on them idk what to do about them(2 votes)
- If the exponents aren't the same, you can't combine them and they can be left alone (i.e. written in the final answer).

We have x^6, but no other term with degree 6, so this term is left alone. We have 9x^4 + 3x^4, which is 9 + 3 = 12x^4. No other terms from here can be combines because we have 2x^5, 4x^2, -x, and 3. So, the final answer should look something like x^6 + 2x^5 + 12x^4 -4x^2 - x - 3. Also remember to write in descending order of degree (highest degree to lowest).(5 votes)

- For the expressions (x+y) squared and x squared +y squared are they equal for all real numbers x and y?(2 votes)
- No. (x+y)² does NOT equal x² + y²

(x+y)² = x² + 2xy + y²(2 votes)

## Video transcript

We're asked to simplify 5x
squared plus 8x minus 3 plus 2x squared minus 7x plus 13x. So really, all we have to do
is we have to combine like terms-- terms that have x raised
to the same power. And the first thing we can do,
we can actually get rid of these parentheses right here,
because we have this whole expression, and then we're
adding it to this whole expression. The parentheses really don't
change our order of operations here. So let me just rewrite it once
without the parentheses. So we have 5x squared plus 8x
minus 3 plus 2x squared. If this was a minus then we'd
have to distribute the negative sign, but it's not. So plus 2x squared minus
7x plus 13x. Now let's just look at the
different terms that have different degrees of x. Let's start with the x squared
terms. So you have a 5x squared term here and you have a
2x squared term right there. So 5 of something plus 2 of that
same something is going to be 7 of that something. So that's going to
be 7x squared. And then let's look at
the x terms here. So we have an 8x right there. We have a minus 7x. And then we have a plus 13x. So if you have 8 of something
minus 7 of something, you're just going to have 1
of that something. And then if you add 14 of
that something more, you're going to 15. So this is going
to be plus 15x. 8x minus 7x-- oh, sorry. You're going to have 14x. 8 minus 7 is 1 plus 13 is 14. Plus 14x. That's these three terms.
8x minus 7x plus 13x. And then finally, you have a
negative 3-- or minus 3, depending on how you
want to view it. And that's the only
constant term. You could say it's x
times x to the 0. But it's a constant term. It's not be multiplied by x. And that's the only one
there, so minus 3. And we've simplified it
as far as we can go. We are done.