6. Let P be a non-zero polynomial such that P(1 + x) = P(1 – x) for all real x and P(1) = 0. Let m be the largest integer such that (x – 1)" divides P(x) for all such P(x). Then, m equals %3D

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A: We will use repeated differentiation to prove this

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A: The answer is false .

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A:

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Q: Show that the following polynomials are irreducible over Q. (a) f(r) = 13r + 15a + 20a? + 21a + 19…

A:

Q: 5. Obtain a polynomial P(x) such that f(x) = P₁(x) given the table -1 -3 x₁ f(x₂) -2 -13 1 -1 2 -9 3…

A:

Q: Consider the set S = {x² + 1, 2x – 2, – x² + x}. The set S spans P2. If t(x) 2x? – 13x + 9 € P2 ,…

A:

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A: We have to solve given problem:

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A:

Q: The polynomial f(x) = x2021 + x2020 +9.03x + 1 has at least one real root.

A: Explanation of the answer is as follows

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.