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10th Class Mathematics Related to Competitive Exam Question Bank Algebra

  • question_answer
    \[{{x}^{3}}+a{{x}^{2}}-7x-6\] can be factorised into 3 linear factors when

    A)  a = 0                                       

    B)  a = 1

    C)  a = 2                     

    D)         a = 3

    Correct Answer: A

    Solution :

     Putting\[a=0\], we have given expression                 \[={{x}^{3}}-7x-6\]                 \[={{x}^{3}}-x-6x-6\]                 \[=x({{x}^{2}}-1)-6(x+1)\]                 \[=(x+1)[x(x-1)-6]\]                 \[=(x+1)[{{x}^{2}}-3x+2x-6]\]                 \[=(x+1)[x(x-3)+2(x-3)]\]                 \[=(x+1)(x+2)(x+3)\] Hence, the given expression can be factorised into \[3\] linear factors when\[a=0\].


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