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Math Help - Remainder Theorm

  1. #1
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    Remainder Theorm

    1. Given: f(x) = x^n+y^n. for which value(s) of n is x+y a factor of f(x)

    2. 2x^3-x^2-2x+2 = (2x-1).Q(x)+R(x) for all values of x. What is the value of R?

    3. if x^3 + kx^2 -3 is divided by x+2 the remainder is 3 more than the remainder when the same expression is divided by x-1. find the value of k
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by Yolo View Post
    1. Given: f(x) = x^n+y^n. for which value(s) of n is x+y a factor of f(x)
    x+y=x-(-y) is a factor of f(x) iff -y is a root of f. When is this possible ? (consider the two cases n even and n odd)
    2. 2x^3-x^2-2x+2 = (2x-1).Q(x)+R(x) for all values of x. What is the value of R?
    What does the remainder theorem tells us about the degree of R(x) ?
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