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Math Help - Polynomial Division

  1. #1
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    Polynomial Division

    I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

    Here is the right answer:

    -4x^2 - 3x - 3 remainder -7

    How can this be?

    Can you show me step by step why the above answer is correct?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by magentarita View Post
    I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

    Here is the right answer:

    -4x^2 - 3x - 3 remainder -7

    How can this be?

    Can you show me step by step why the above answer is correct?
    My method may not be like yours, but I can't manage to change it ~~

    -4x^3+x^2-4 and x-1.

    First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x.
    -4x^3={\color{green}-4x^2}(x).

    So I'll write :
    -4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4

    And so on... :

    -4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4

    (x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4 =\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}}


    If you want to know where your mistake(s) is/are, just show your work ^^
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  3. #3
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    Perfect!

    Quote Originally Posted by Moo View Post
    Hello,

    My method may not be like yours, but I can't manage to change it ~~

    -4x^3+x^2-4 and x-1.

    First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x.
    -4x^3={\color{green}-4x^2}(x).

    So I'll write :
    -4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4

    And so on... :

    -4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4

    (x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4 =\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}}


    If you want to know where your mistake(s) is/are, just show your work ^^
    Perfectly done!
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