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Polynomials restricted by their degree
Let P2(R#) represent the set of all polynomial functions of degree no greater than 2,
that is, functions that can be written in the form ax2 + bx + c, with a, b, and c being
real numbers, let the operation + represent polynomial addition, and let the operation
* represent polynomial multiplication.
a. Demonstrate or explain why the system (P2(R#), +) is a commutative group, that is,
demonstrate or explain why:
i. (P2(R#), +) is closed
ii. (P2(R#), +) is associative
iii. (P2(R#), +) has an identity element, i.e., an additive identity
iv. Each element in P2(R#) has an additive inverse
v. (P2(R#), +) is commutative
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Demonstrate or explain why the system (P2(R#), *) is NOT a semi-group, that is,
demonstrate or explain why:
i. (P2(R#), *) is NOT closed, or
ii. (P2(R#), *) is NOT associative
Demonstrate or explain why the system (P2(R#), *) is NOT a semi-group, that is,
demonstrate or explain why:
i. (P2(R#), *) is NOT closed, or
ii. (P2(R#), *) is NOT associative
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