2. Let D be an integral domain and let D[X] denote the ring of polynomials in the indeterminate X and coefficients coming from D. For a nonzero polynomial f(x) € D[X], let deg f(X) denote the degree of the the polynomial f(x). a. Prove that the constant term of the product f(X)g(X) is the product of the constant terms of f(X) and g(X). b. Prove that the leading coefficient of the product f(X)g(X) is the product of the leading coefficients of f(X) and g(X). c. Prove that deg f(X)(g(X) = deg f(X) + deg g(X).

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Q: The set C1(R) ⊂C(R) is the set of differentiable real-valued functions with domain R. Consider C1(R)…

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Q: Let F be a field of characteristic # 2. Let a and ß be roots of X2 - ae F(X) and X² − b e F(X),…

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Q: If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-3)g(-3)…

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Q: let f(z) be polynomial of degree at least two. show that |f(z)|>|z| for large |Z|.

A: We prove this result by contradiction.

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Q: 3. Let P(x) be a polynomial of degree n. If n is even, prove P(x) cannot have an inverse function.

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Q: 3. Let x0, x₁,...,xn be distinct points on the interval [a, b], where Xo <x₁ < x₂ <... < xn and let…

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Q: f = x² + x³x²+1, g = x³ + 1 in Q[x];

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Q: rove or Disprove that the polynomial x⁴ − 2 ∈ Q[x] is solvable by radical over Q

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Q: OJennifer Findley Write an approximate measure for each angle shown.

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Q: f(x) = x² − 3 is the minimal polynomial of √3 over Q,

A: We have that              f(x) = x2-3  be a polynomial of two degree.