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Adding polynomials

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

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  • blobby green style avatar for user Madhumitha Rangaraj
    At , 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)
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  • aqualine ultimate style avatar for user Janiya Fu
    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)
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  • blobby green style avatar for user Sacia Ashe
    Why do you have to distribute a negative?
    (4 votes)
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  • old spice man blue style avatar for user angper23
    how would you combine the terms if they had different exponents
    (5 votes)
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  • male robot johnny style avatar for user gilesitis
    Why didn't he add the exponents when he added 5x squared + 2x squared?
    (2 votes)
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    • blobby green style avatar for user hannahrosepanzer
      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)
  • old spice man green style avatar for user hyah21
    Is the process the same when you are subtracting?
    (4 votes)
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  • male robot hal style avatar for user Bork Doggo
    me looking at these questions that were commented years ago and the nostalgia comes of doing khan academy
    (5 votes)
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  • blobby green style avatar for user vapsy36198
    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)
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    • female robot grace style avatar for user loumast17
      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)
  • aqualine ultimate style avatar for user Caleb Tinoco
    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)
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    • old spice man green style avatar for user Elijah Daniels
      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)
  • blobby green style avatar for user Shaun Flak
    For the expressions (x+y) squared and x squared +y squared are they equal for all real numbers x and y?
    (2 votes)
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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.