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Finding an error in polynomial subtraction

Sal analyzes a polynomial subtraction process to find the step that has an error.

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  • blobby green style avatar for user NITHESH KUMAR
    I am very happy to be a part of these course. This course is very useful to me, apart from that its make me intersting on maths.

    Here i would like to ask so many questions.
    1. Why polynomial equation has exponents?
    2. Why exponents should not be negative integer or fraction?
    3. What is the significance of exponents in polynomial equation?

    I am eagerly waiting for your reply. it would be more helpful to my rest of the questions..
    (3 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user AD Baker
      1) A polynomial does not require an exponent. '6', '-8', '5x', and '-22y' are all polynomials (a special type of polynomial called a monomial).

      2) By definition a polynomial can only contain non-negative integers. This is topic for more advanced mathematics and it has to do with how polynomials are used as functions.

      3. Exponents are used to determine the degree of a polynomial. The largest exponent in the expression determines the degree. x^2 + 6 is a second degree polynomial. y^8 - 17y^5 + 4y^2 -9 is an eighth degree polynomial.
      (4 votes)
  • leaf blue style avatar for user EntitledGraduate
    So we're substituting certain properties by replacing a negative and/or a positive sign based on the problem?
    (1 vote)
    Default Khan Academy avatar avatar for user

Video transcript

- [Voiceover] Kenisha is asked to subtract seven B squared minus five B plus one from two B squared plus three B plus 11. Her work is shown below and we see all the steps that she took. And then they say at which step did Kenisha make an error? And it's pretty clear she made an error, because they're not giving us an option that she didn't make an error. So let's see what went on here. So the first thing is, we want to subtract seven B squared minus five B plus one, we want to subtract that from two B squared plus three B plus 11. And we see that in step one she set it up properly. She is indeed subtracting, she is indeed subtracting seven B squared minus five B plus one from two B squared plus three B plus 11. That's fair. Alright, so step one seems to be okay. Now let's see step two, it looks like she's going to distribute the negative sign, so the negative of seven B squared is, as you can see is negative seven B squared. We're gonna subtract seven B squared. And then you have the negative of negative five B. Well that's going to be positive five B. So this right over here, this one over here should, this over here should be a positive five B. Let me do that in a new color. So this should be a positive five B. And then the negative of positive one, this should be a negative one. That should be a negative one right over there. So she's making a mistake, she's making a mistake in step two when she distributes this negative sign. So step two is where she made, is where she actually made her error. From there it seem reasonable, she is subtracting the coefficients on the B squared terms, so two B squared minus seven B squared, gets us this right over there. Then on the B terms, you have three B and then, let's see, you have, it should be three B plus five B if she distributed the negative sign right, but since she didn't distribute the negative sign right, she has three B minus five B. And it should be 11 minus one, but since she didn't do the distribution correctly, we have 11, it should be 11 minus one, as we said before, because you're gonna distribute this negative sign, but she left that as a plus one and so that's why she got that over there. So her real mistake was clearly in step two. 'Cause from there on she's doing reasonable things, it's just she made that one error.