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Rajan@2021
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Use factor theorem to factorize the following polynomials completely. x 3 +2x 2 -5x -6

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We have been asked to find to factorize the following polynomials completely, using factor theorem in the given polynomial
x3+2x25x6

Book – ML Aggarwal, Avichal Publication, factorisation, chapter 6, question no 15(i)

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  1. To find a factor of f(x) we assume different values of x and substitute it in f(x)

    First we consider the factors of the constant term −6 i.e., ±1,±2,±3,±6
    Now we substitute the values of x in f(x)
    If f(x)=0 for some value a
    Then (x−a) is a factor of f(x)
    [Note : This is a hit and trial method, So you have to iterate the process until you get the required x]

    Substituting  x=−1 in f(x) , We get,
    f(−1)=(−1)3+2(−1)2−5(−1)−6
    =−1+2(1)+5−6
    =−1+2+5−6
    =−7+7
    =0
    ∴ By factor theorem,
    (x+1) is a factor of f(x)

    Now dividing f(x) by (x+1), we get
    x3+2x2−5x−6=(x+1)(x2+3x−2x−6)=(x+1){x(x+3)−2(x+3)}=(x+1)(x−2)(x+3)

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