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Math Help - Ordering Polynomials

  1. #1
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    Ordering Polynomials

    I have a homework paper that's due tomorrow, and it has to be 100% correct to earn credit. I have everything correct except for two problems. My teacher said that the terms weren't in the correct order, but I have no idea what the correct order would be. I'd really appreciate some quick help.

    1) (x - 2y)(3x^2 - 2xy + 6y^2)

    My answer is: 3x^3 - 8x^2y + 16xy^2 - 12y^3

    2) (2 - x)(3 - 4x)

    My answer is: 4x^2 - 11x + 6

    Thanks for your time.
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  2. #2
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    It's common to write from the highest power descending to the lower ones. You should write the powers of 3 first, then 2, etc.
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  3. #3
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    Quote Originally Posted by Jameson
    It's common to write from the highest power descending to the lower ones. You should write the powers of 3 first, then 2, etc.
    I actually did that the first time. My first answers were:

    1) 3x^3 - 12y^3 - 8x^2y + 16xy^2

    2) 4x^2 - 11x + 6

    However, she marked those two wrong. On a related note, there was another, similar problem which I got correct.

    3) (3x^2 - 5y^2)(2x - 4y)

    My correct answer was: 6x^3 - 12x^2y - 10xy^2 + 20y^3

    After seeing that problem 3 was correct, but problem 1 was wrong, I tried to reorder my terms in problem 1 in the same way as I did in problem 3 ( x^3 first, then x^2y, then xy^2, then y^3). However, she still marked it wrong. So, I'm completely stuck. Any more tips?
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  4. #4
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    Quote Originally Posted by greenstupor
    I actually did that the first time. My first answers were:

    1) 3x^3 - 12y^3 - 8x^2y + 16xy^2

    2) 4x^2 - 11x + 6

    However, she marked those two wrong. On a related note, there was another, similar problem which I got correct.

    3) (3x^2 - 5y^2)(2x - 4y)

    My correct answer was: 6x^3 - 12x^2y - 10xy^2 + 20y^3

    After seeing that problem 3 was correct, but problem 1 was wrong, I tried to reorder my terms in problem 1 in the same way as I did in problem 3 ( x^3 first, then x^2y, then xy^2, then y^3). However, she still marked it wrong. So, I'm completely stuck. Any more tips?
    The ordering in your first answer is correct, the multiplication is wrong.

    Generally when ordering, put the highest powers first, as you did. Typically you then "alphabetize" the answer by putting higher powers of a before b. For example if you have a^2c^3+6a^2b^3 you write 6a^2b^3+a^2c^3 because b comes before c. That's why your re-ordering is "more correct."

    -Dan
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  5. #5
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    Thanks for the help.
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