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Difference of two squares considered to be a quadratic

  1. Aug 20, 2011 #1
    1. The problem statement, all variables and given/known data
    is an expression that is a difference of two squares considered to be a quadratic. For example, would x2 - 4 be a quadratic? What about x4 - 4?


    2. Relevant equations
    Ax2 + Bx + C


    3. The attempt at a solution
    I know we can factor a DOTS into two binomials like a quadratic in the for Ax2 + Bx + C, but I wanted to be clear on what a DOTS was relative to a quadratic equation.
     
  2. jcsd
  3. Aug 20, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Dots

    "Quadratic" simply means "a polynomial of degree 2". Yes, [itex]x^2- 4[/itex] is quadratic, no, [itex]x^4- 4[/itex] is not. The importance of the "difference of two squares" is, as you say, that it can be easily factored: the quadratic [itex]x^2- 4[/itex] can be factored into two linear factors: [itex](x- 2)(x+ 2)[/itex], the quartic [itex]x^4- 4[/itex] can be factored into two quadratic terms: [itex](x^2- 2)(x^2+ 2)[/itex].
     
  4. Aug 24, 2011 #3
    Re: Dots

    So, to be clear, x4 - 4 is a quartic. Is there a special name given to something like x6 - 4?
     
  5. Aug 24, 2011 #4

    Mark44

    Staff: Mentor

    Re: Dots

    I haven't seen any terminology for polynomials higher than degree five, and these are called quintics.
     
  6. Aug 24, 2011 #5
    Re: Dots

    Interesting. I'll be on the lookout :smile:
     
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