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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    When \[p(x)={{x}^{3}}+a{{x}^{2}}+2x+a\]is divided by \[(x+a).\] the remainder is ___.

    A)  0                    

    B)         a        

    C)  -a                   

    D)         2a       

    Correct Answer: C

    Solution :

    We have, \[p(x)={{x}^{3}}+a{{x}^{2}}+2x+\] By remainder theorem, we know that when \[p(x)\]is divided by \[(x+a).\]then the remainder is \[(p-a).\]Now, \[p(-a)={{(-a)}^{3}}+a{{(-a)}^{2}}+2(-a)+a\] \[=-{{a}^{3}}+{{a}^{3}}-2a+a=-a\]


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