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Math Help - LCM and HCF of Algebric Expressions

  1. #1
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    LCM and HCF of Algebric Expressions

    ,
    What is the method to find the LCM and HCF of the following expressions?
    x^3 - 2x^2 - 13x -10 and x^3 - x^2 -10x - 8
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  2. #2
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    P(x)=x^3 - x^2 -10x - 8 \ and \ Q(x)=x^3 - 2x^2 - 13x -10
     factors\ of\ P(x) =(x+1)(x+2)(x+4)
     factors\ of\ Q(x) =(x+1)(x+2)(x-5)
     common\ factors\ of\ P(x)\ and\ Q(x) = (x+1),(x+2),(x+1)(x+2)

    Highest Common Factors (HCF) of P(x) and Q(x)   =(x+1)(x+2)



    since \ (LCM)\ of \ P(x) \ and \ Q(x)= \frac{P(x) \times Q(x)}{HCF}

     \ LCM =\frac{(x+1)(x+2)(x+4) \times (x+1)(x+2)(x-5)}{(x+1)(x+2)}

     Least\ common\ multiplier\ (LCM)\ of\ P(x)\ and\ Q(x)=(x+1)(x+2)(x+4)(x-5)
    Last edited by ramiee2010; October 6th 2009 at 05:03 AM. Reason: correction
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  3. #3
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    Quote Originally Posted by saberteeth View Post
    ,
    What is the method to find the LCM and HCF of the following expressions?
    x^3 - 2x^2 - 13x -10 and x^3 - x^2 -10x - 8
    Factor each, and then make a table with the factors:

    [HTML]P(x): (x + 1)(x + 2)(x + 4)
    Q(x): (x + 1)(x + 2) (x - 5)
    ----------------------------------
    LCM: (x + 1)(x + 2)(x + 4)(x - 5)
    HCF: (x + 1)(x + 2)[/HTML]
    The LCM is the product of all the factors; the HCF (or GCF, for Americans) is the product of only the common factors.
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  4. #4
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    Quote Originally Posted by ramiee2010 View Post
    P(x)=x^3 - x^2 -10x - 8 \ and \ Q(x)=x^3 - 2x^2 - 13x -10
     factors\ of\ P(x) =(x+1)(x+2)(x+4)
     factors\ of\ Q(x) =(x+1)(x+2)(x-5)
     common\ factors\ of\ P(x)\ and\ Q(x) = (x+1),(x+2),(x+1)(x+2)

    Highest Common Factors (HCF) of P(x) and Q(x)   =(x+1)(x+2)



    since \ (LCM)\ of \ P(x) \ and \ Q(x)= \frac{P(x) \times Q(x)}{HCF}

     \ LCM =\frac{(x+1)(x+2)(x+4) \times (x+1)(x+2)(x-5)}{(x+1)(x+2)}

     Least\ common\ multiplier\ (LCM)\ of\ P(x)\ and\ Q(x)=(x+1)(x+2)(x+4)(x-5)
    Thanks, i got it. But, how did you find the factors so accurately? What method did you use?
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  5. #5
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    Quote Originally Posted by saberteeth View Post
    ...how did you find the factors so accurately? What method did you use?
    To learn how to factor polynomials, try here.
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  6. #6
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    Cool. Just what i needed.
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