The remainder of f(x)/(x^2+x+1) and f(x)/[(x+1)^2] are x+5 and x-1 respectively.?

What is the remainder of f(x)/[(x^2+x+1)(x+1)]?

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  • 8 years ago
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    We have

    f(x) = P(x)(x^2+x + 1)+ (x+5) ,,(1)

    _

    and f(x) = Q(x)(x+1)^2 + (x-1) = (Q(x)(x+1) +1)(x +1) - 2 ..(2)

    now f(x) divided by (x^2+x+1)(x+1) the remainder shall be a quadratic polynomial say

    A(x^2 + x + 1) + Bx + C

    from (1) B= 1 and C = 5

    so remainder = A(x^2+x + 1) + x + 5

    from (2) we should have A + 4 = - 2 or A = - 6

    so remainder = - 6 x^2 - 5 x -1

  • Anonymous
    8 years ago

    Hello Gabriel,

    I have posted a full solution to your question at one of the math help forums I help to moderate so that I may give you an easy to read explanation using LaTeX:

    http://www.mathhelpboards.com/f52/gabriels-questio...

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