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Rajan@2021
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When divided by x−3 the polynomials x 3 −px 2 +x+6 and 2x 3 −x 2 −(p+3)x−6 leave the same remainder. Find the value of ′ p ′

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We have to find the value of p in the given polynomial when divided by x3 leave the same remainder using remainder theorem

ML Aggarwal Avichal Publication Factorisation chapter 6, question no 8(i)

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  1. The Remainder is same whne (x−3) divides (x
    3
    −px
    2
    +x+6) & (2x
    3
    −x
    2
    −(p+3)x−6)
    ∴ Using Remainder Theorem
    R(3)=x
    3
    −px
    2
    +x+6
    =3
    3
    −p(3
    2
    )+3+6
    =27−9p+3
    =36−9p

    R(3)=2x
    3
    −x
    2
    −(p+3)x−6
    =2(3
    3
    )−3
    2
    −(p+3)3−6
    =2×27−9−3p−9−6
    =54−24−3p
    =30−3p

    Remainder are same
    ∴36−9p=30−3p

    36−30=−3p+9p

    6=6p

    1=p

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