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Homework Help: Simple factoring question

  1. Jan 23, 2009 #1
    1. The problem statement, all variables and given/known data

    can u factor x2+4
    and cant seem to remember the the difference of cubes and isn't there another special cubed theorem.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 23, 2009 #2


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    It can be factored but it won't be factored with real numbers. You'd need to introduce the imaginary constant,i, such that i2=-1 and use that to factor.
  4. Jan 23, 2009 #3


    Staff: Mentor

    x2 + 4 = (x + 2i)(x - 2i), where i is the imaginary unit rock.freak667 mentioned.
    Here are the sum and difference of cubes formulas:
    x3 + a3 = (x + a)(x2 - ax + a2)
    x3 - a3 = (x - a)(x2 + ax + a2)
  5. Jan 23, 2009 #4
    thanks, so i have another question if someone can help me.

    lim x3-62+11x-6
    x->-1 x3-4x2-19x +14
    i cant seem how to factor the top out if i even need to do that or the bottom
  6. Jan 23, 2009 #5


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    Why would you need to factor it? Did you evaluate it at x=-1? Was it in the indeterminate form 0/0?
  7. Jan 23, 2009 #6


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    If the numerator, or denominator, goes to zero when x = 1, then (x-1) is a factor.

    You can factor it out by dividing (x-1) into the numerator, say, in the style of long-division.
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