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Rajan@2021
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If (x + 2) and (x + 3) are factors x3 + ax + b, find the values of ‘a’ and ‘b’. With these values of a and b factorise the given expression

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Factorise the given expression if (x + 2) and (x + 3) are factors x3 + ax + b, and we need to determine the values of ‘a’ and ‘b’. With  values of a and b we have to factorize the given polynomial completely

ML Aggarwal Avichal Publication, Factorisation, chapter 6, question no 23

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  1. Given polynomial is p(x)=x3+ax+b

    x+2 is a factor
     2 is a root of the polynomial.
    (2)3+a(2)+b=0
    2a+b=8
    x+3 is a factor
    3  is a root of the polynomial.
    (3)3+a(3)+b=0
    3a+b=27
    Solving the above equations,
    we get a=19, b=30

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