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Functions 12U - Basic Polynomial questions

  1. Oct 19, 2008 #1
    Problem One
    1008 = [(10+x)(10+x)(5+x)] / 2

    Solution Attempt
    5004=[(10+x)(10+x)(5+x)]

    5004= (100+10x+10x+x^2)(5+x)

    5004= 500 + 50x + 5x^2 + 100x + 20x^2 + x^3

    5004 = x^3 + 25x^2 + 150x + 500

    0 = x^3 + 25x^2 + 150x - 4504

    Where do I go from here?

    Problem Two
    Solve.
    x^4 - 10x^2 + 16 = 0

    Solution Attempt
    I have no idea on this one. What kind of factoring can i use when the first and second parts are ^4 and ^2 respectively, with the last part being a regular number?


    Thanks in advanced guys, I know it's probably something little i'm overlooking :)
     
  2. jcsd
  3. Oct 19, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    For the second one factor it like it was u^2-10u+16 where u=x^2. For the first one, I think there may be multiple mistakes. How did 1008 turn into 5004?
     
  4. Oct 19, 2008 #3
    Alright, thanks for the help :)

    Typo on the first one, let me try again ;)

    Problem One
    1008 = [(10+x)(10+x)(5+x)] / 2

    Solution Attempt
    504=[(10+x)(10+x)(5+x)]

    504= (100+10x+10x+x^2)(5+x)

    504= 500 + 50x + 5x^2 + 100x + 20x^2 + x^3

    504 = x^3 + 25x^2 + 150x + 500

    0 = x^3 + 25x^2 + 150x - 4

    Where do I go from here?
     
  5. Oct 20, 2008 #4
    Again you are making mistakes. Remember its a divide by two on the RHS. So when you shift it to the LHS, it becomes a multiply by two. It thus becomes 1008*2 and NOT 1008/2.

    Then, do you know how to factorize third degree polynomials?
     
  6. Oct 20, 2008 #5
    Righto I missed that one, so the next lines should be:

    2016 = x^3 + 25x^2 + 150x + 500

    0 = x^3 + 25x^2 + 150x -1516

    Then I would just use factor theorem to solve for x, does that work out in this case?
     
  7. Oct 20, 2008 #6
    solve slowly....dont need to hurry..... dont make so many mistakes

    (10 + x)*(10+x)(5+x) = (5+x)(x^2 + 20x + 100) = 5x^2 + 100x + 500 + x^3 + 20x^2 + 100x

    = x^3 + 25x^2 + 200x + 500.....check it!!
     
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