document.write( "Question 262821: Consider any integer x. The next consecutive integer can be represented by the binomial (x+1).\r
\n" ); document.write( "\n" ); document.write( "a. write a polynomial for the sum of any two consecutive integers\r
\n" ); document.write( "\n" ); document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #193587 by drk(1908)\"\" \"About 
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(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
\n" ); document.write( "SUM = x + x + 1 = 2x + 1.
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\n" ); document.write( "(part b):
\n" ); document.write( "CASE 1: Let the first number, x, be even. Then the next consecutive number, x+1, is odd.
\n" ); document.write( "Sum of x + x + 1 = even + odd = 2x + 1.
\n" ); document.write( "Notice that we cannot divide each term by 2. This means that an even + odd is odd.
\n" ); document.write( "CASE 2: Let the first number, x, be odd. Then the next consecutive number, x+1, is even.
\n" ); document.write( "Sum of x + x + 1 = odd + even = 2x + 1.
\n" ); document.write( "Notice that we cannot divide each term by 2. This means that an odd + even is odd.
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\n" ); document.write( "So, the sum of 2 consecutive integers must always be odd. \n" ); document.write( "
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