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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If \[(x-1)\] is a factor of polynomial \[f(x)\] but not of\[g(x)\], it must be a factor of which of the following polynomials?

    A) \[f(x)\,\,g(x)\]                 

    B) \[-f(x)+g(x)\]     

    C)        \[f(x)-g(x)\]        

    D)        \[\{f(x)-g(x)\}g(x)\]                     

    Correct Answer: A

    Solution :

    Given\[(x-1)\]is a facto r of \[f(x),\]but not of \[g(x)\] \[\Rightarrow \]\[f(1)=0\]and \[g(1)\ne 0\] \[\therefore \]Or the given options \[(x-1)\]must be a factor of \[f(x)g(x).\] Since, (1) \[g(1)=0\]as \[f(1)=0\]


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