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Using the Remainder and Factor Theorem, factorise the following polynomial: x 3 +10x 2 −37x+26

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An important question from factorisation chapter for examination as it has been already asked in previous year paper of 2014 in which we asked to factorise the following polynomial: x3+10x237x+26 using factor and remainder theorem 

ML Aggarwal Avichal Publication chapter 6, question no 17


1 Answer

  1. Let f(x)=x3+10x237x+26
    Putting x=1,

    we get
     By factor theorem, x1 is factor of f(x).
    On dividing x3+10x237x+26 by x1,

    we get x2+11x26 as the quotient and remainder =0.
     The other factor of f(x) are the factor of x2+11x26
    Now, x2+11x26
    Hence, x3+10x237x+26=(x1)(x2)(x+13)

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