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I Question About Long Division of Polynomials

  1. Jun 15, 2016 #1
    Dividend: 4x^3 - 6x - 11
    Divisor: 2x - 4

    In this problem above, the dividend lacks a variable to the second power, so we have to add a 0x^2 to make it:

    4x^3 + 0x^2 - 6x - 11

    Question:

    Why do we add 0x^n? (n = missing powers)

    In regular long division, we do no such thing. Why do we have to add these extra variables into the dividend in polynomial long division?

    TVM!
     
  2. jcsd
  3. Jun 15, 2016 #2

    fresh_42

    Staff: Mentor

    I don't know. I don't.

    Edit: It is probably to help perform the subtraction. If you don't add it you subtract from zero anyway. So writing it might help to avoid mistakes.
     
  4. Jun 15, 2016 #3
    Like the post above says, I think it's only to avoid error ( especially while learning it as a student). Wouldn't actually affect your answer in any way.
     
  5. Jun 15, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You "add" 0, which means you do not change anything. In regular long division, the 0 would be there already to indicate the right places, in polynomials, you don't need to write +0x2 explicitely because every term has its meaning independent of where it is located.
     
  6. Jun 15, 2016 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Sure we do. That's what zero is for.

    If you want to do long division of 3065 by 42, the place value system we use to write decimal numerals is as follows:

    3065 = 3 × 103 + 0 × 102 + 6 × 101 + 5 × 100

    or

    3065 = 3x3 + 0x2 + 6x + 5, where it is understood x = 10.

    It's a similar situation when certain terms are missing from a polynomial dividend.
     
  7. Jun 16, 2016 #6
    Got it! Thanks.
     
  8. Jun 18, 2016 #7
    wow. Did not see that either. thank you
     
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