Question 262821: Consider any integer x. The next consecutive integer can be represented by the binomial (x+1).
a. write a polynomial for the sum of any two consecutive integers
b. explain how you can be sure that the sum of any two consecutive integers is always odd. Use the polynomial form part (a) in your explanation
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! (part a) If the first integer is x and the next consecutive integer is (x+1), then the sum of two consecutive integers can be expressed as
SUM = x + x + 1 = 2x + 1.
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(part b):
CASE 1: Let the first number, x, be even. Then the next consecutive number, x+1, is odd.
Sum of x + x + 1 = even + odd = 2x + 1.
Notice that we cannot divide each term by 2. This means that an even + odd is odd.
CASE 2: Let the first number, x, be odd. Then the next consecutive number, x+1, is even.
Sum of x + x + 1 = odd + even = 2x + 1.
Notice that we cannot divide each term by 2. This means that an odd + even is odd.
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So, the sum of 2 consecutive integers must always be odd.
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