Exercise 2.1.2: Mathematical expressions that evaluate to even and odd integers. In the expressions below, n is an integer. Indicate whether each expression has a value that is an odd integer or an even integer. Use the definitions of even and odd to justify your answer. You can assume that the sum, difference, or product of two integers is also an integer. a) 10n3 + 8n - 4 b) -2n2 - 5 An answer and justification are required. Definition 2.1.1: Even and odd integers.An integer x is even if there is an integer k such that x = 2k.An integer x is odd if there is an integer k such that x = 2k+1.

Algebra: Structure And Method, Book 1
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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
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Chapter3: Solving Equation And Problems
Section3.8: Proof In Algebra
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Exercise 2.1.2: Mathematical expressions that evaluate to even and odd integers.

In the expressions below, n is an integer. Indicate whether each expression has a value that is an odd integer or an even integer. Use the definitions of even and odd to justify your answer. You can assume that the sum, difference, or product of two integers is also an integer.

a) 10n3 + 8n - 4

b) -2n2 - 5

An answer and justification are required.

Definition 2.1.1: Even and odd integers.
An integer x is even if there is an integer k such that x = 2k.
An integer x is odd if there is an integer k such that x = 2k+1.

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