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Determine a constant k such that the polynomial P(x, y, z) = x^5 + y^5 + z^5 + k(x^3+y^3+z^3)(x^2+y^2+z^2) is divisible by x+y+z.
Let f(x) be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of f(x) is 6.
(a) Is it possible for x=3 to be a root of f(x)?
(b) Is it possible for x=3 to be a double root of f(x)? Prove your answers.
Is there a way to prove this question with the Rational root theorem?
Edit 2: I solved (a) but I'm not sure how to solve part (b)
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