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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    The value of \[{{(x-a)}^{3}}+{{(x-b)}^{3}}+{{(x-c)}^{3}}\]\[-3(x-a)(x-b)(x-c),\]when \[a+b+c=3x\]is ______.

    A)  3                                

    B)  2        

    C)  1                    

    D)         0

    Correct Answer: D

    Solution :

    It is given that \[a+b+c=3x.\]Then, \[{{(x-a)}^{3}}+{{(x-b)}^{3}}+{{(x-c)}^{3}}-3(x-a)(x-b)(x-c)\] \[=(x-a+x-b+x-c)[{{(x-a)}^{2}}+{{(x-b)}^{2}}\] \[+{{(x-c)}^{2}}-(x-a)(x-b)-(x-b)(x-c)\] \[-(x-c)(x-a)]=0\]


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