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Factor theorem

  1. Aug 10, 2011 #1
    1. The problem statement, all variables and given/known data

    show that (x-2) is a factor of x^3 - 2x^2 + x - 2

    2. Relevant equations



    3. The attempt at a solution

    f(2) = 2^3 - 2(2)^2 + 2 - 2

    is that any good
     
  2. jcsd
  3. Aug 10, 2011 #2

    Mark44

    Staff: Mentor

    What does 2^3 - 2(2)^2 + 2 - 2 simplify to?
     
  4. Aug 10, 2011 #3
    = 8 - 8 + 2 - 2
    = 0
     
  5. Aug 10, 2011 #4

    Mark44

    Staff: Mentor

    OK, that's better. Now, you have f(2) = 0, where apparently f(x) = x^3 - 2x^2 + x - 2. If f(a) = 0, what does that tell you about x - a being a factor of f(x)?
     
  6. Aug 10, 2011 #5
    that it is a factor of the equation
     
  7. Aug 10, 2011 #6

    Mark44

    Staff: Mentor

    That x - 2 is a factor of x^3 - 2x^2 + x - 2.

    Note that x^3 - 2x^2 + x - 2 is not an equation (there's no equal sign).
     
  8. Aug 10, 2011 #7
    oh ok, got it
     
  9. Aug 11, 2011 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    There is nothing stopping you dividing x^3 - 2x^2 + x - 2
    by x-2
    and showing that there is 0 remainder.

    Can you do that? Try it like you'd do long division, where the first "digit" of the answer will be x^2.


    x-2 ) x^3 - 2x^2 + x - 2
     
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