10th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    The polynomial \[{{\text{a}}^{\text{3}}}-\text{3}{{\text{a}}^{\text{2}}}+\text{a}+\text{2}\]is divided by a polynomial g[a].The quotient and remainder obtained are (a - 2) and (-2a + 4) respectively. Find g[a].

    A)  \[{{\text{a}}^{\text{2}}}+\text{a}+\text{1}\]      

    B)         \[{{\text{a}}^{\text{2}}}-\text{a}+\text{1}\]

    C)  \[{{\text{a}}^{\text{2}}}-\text{a}-\text{1}\]       

    D)         \[{{\text{a}}^{\text{2}}}+\text{a}-\text{1}\]

    Correct Answer: B

    Solution :

     Let\[\text{216 }=\text{ 192 }\times \text{ 1 }+\text{ 24}\] \[\text{192 }=\text{ 24 }\times \text{ 8 }+\text{ }0\]and\[{{6}^{x}}\] Then\[{{6}^{x}}={{(2\times 3)}^{x}}={{2}^{x}}\times {{3}^{x}}\] \[\Rightarrow \]\[{{6}^{x}}\] Hence, \[\therefore \]


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