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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    For what value of k, \[\mathbf{3}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+3k}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+2x+6}\] is exactly divisible by \[\mathbf{(x-2)?}\]

    A)  1                                

    B)  2              

    C)  -2                               

    D)  \[-\frac{8}{3}\]

    Correct Answer: D

    Solution :

    (d): Here, \[x-2=0\Rightarrow x=2\] By Factor Theorem, \[f\left( 2 \right)=0\] \[\Rightarrow 3{{\left( -2 \right)}^{4}}+2{{\left( -2 \right)}^{3}}+3k{{\left( -2 \right)}^{2}}+\left( -2 \right)+6=0\] \[\Rightarrow 48-16+12k-6+6\Rightarrow 12k=-32\] \[\Rightarrow k=\frac{-8}{3}\]


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