consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|15}, b is an integer less than 10, and c is a prime less than 20. how many second degree polynomials can we make in the form y=ax2+bx+c, where a,b,and c are in the given sets?

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A: Let

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Q: e of all polynomials in C[0, ed in C[0, 1] with respect to

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Q: If a polynomial is reducible over Q then it is reducible over Z. O True O False

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Q: 13. Let P(x) be the degree 10 polynomial through the 11 points (-5,5), (-4,5), (-3,5), (-2,5),…

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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Q: *** Let R be a unique factorization domain. Let p E R. If x is irreducible, then it is prime.***

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Q: 1.) Does the following set of polynomials {t2 +1,t? +t,t + 1} span P2?

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Q: 7. Show that each polynomial f(x) such that f(x) is irreducible in Z, (a) 7x + 6x? + 4x + 6 (b)

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.