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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    The value of k for which \[(x+2)\] is a factor of (x \[{{(x+1)}^{7}}+{{(3x+k)}^{3}}\] is ____.

    A)  -7                               

    B)  7                    

    C)  -1                   

    D)        \[-6-{{3}^{(7/3)}}\]                 

    Correct Answer: B

    Solution :

    Let \[f(x)={{(x+1)}^{7}}+{{(3x+k)}^{3}}\] Since,\[(x+2)\] is a factor of\[f(x).\]Therefore, by factor theorem,\[f(-2)=0\] \[\Rightarrow \]\[{{(-2+1)}^{7}}+(3x(-2)+k)3=0\] \[\Rightarrow \]\[{{(-1)}^{7}}+{{(-6+k)}^{3}}=0\Rightarrow {{(-6+k)}^{3}}=1\] \[\Rightarrow \]\[-6+k=1\Rightarrow k=7\]


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