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Need help with this Foundations of Mathematics homework problem. Below the homework problem is my work. I received feedback from my teacher and he said "You're proving that the product of an even and odd integer is even here; you need to prove that the product of two consecutive integers is even."   1. Prove that the product of two consecutive integers is even.   Let m = 2k and n = 2l + 2. Thereby, m and n are two odd integers and k and l are integers. mn = (2k)(2l + 2) =           (2)(k)(2)(l + 1) =           2(2kl + 2k) Proof Two integers which are added or multiplied are also integers, so (2

Need help with this Foundations of Mathematics homework problem. Below the homework problem is my work. I received feedback from my teacher and he said "You're proving that the product of an even and odd integer is even here; you need to prove that the product of two consecutive integers is even."   1. Prove that the product of two consecutive integers is even.   Let m = 2k and n = 2l + 2. Thereby, m and n are two odd integers and k and l are integers. mn = (2k)(2l + 2) =           (2)(k)(2)(l + 1) =           2(2kl + 2k) Proof Two integers which are added or multiplied are also integers, so (2

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
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Need help with this Foundations of Mathematics homework problem. Below the homework problem is my work. I received feedback from my teacher and he said "You're proving that the product of an even and odd integer is even here; you need to prove that the product of two consecutive integers is even."

 

1. Prove that the product of two consecutive integers is even.

 

Let m = 2k and n = 2l + 2. Thereby, m and n are two odd integers and k and l are integers.

mn = (2k)(2l + 2) =

          (2)(k)(2)(l + 1) =

          2(2kl + 2k)

Proof

Two integers which are added or multiplied are also integers, so (2kl + 2k) is an integer also. As a result, 2(2kl + 2) is an odd integer.

This proves that the product of two consecutive integers is even.

 

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