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Rajan@2021
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Show that (x−3) is a factor of x 3 −7x 2 +15x−9. Hence factorize x 3 −7x 2 +15x−9.

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A basic question from factorisation in which we have been asked to show that (x3) is a factor of x37x2+15x9. Hence  we are to factorize the polynomial completely

ML Aggarwal, Avichal Publication, Factorisation, chapter 6, question no 12

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1 Answer

  1. Let us assume
    x−3=0⇒x=3

    Now, f(3)=(3)
    3
    −7(3)
    2
    +15(3)−9
    =27−63+45−9=72−72=0
    ∴ By remainder theorem,
    (x−3) is a factor of f(x)

    Now, dividing f(x) by (x−3), we get
    x
    3
    −7x
    2
    +15−9=(x−3)(x
    2
    −4x+3)
    =(x−3)(x
    2
    −x−3x+3)
    =(x−3){x(x−1)−3(x−1)}
    =(x−3)(x−3)(x−1)
    =(x−3)
    2
    (x−1)

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