Question 1143028
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Note that the wording of the problem doesn't specify that x is the smallest of the three consecutive integers.  The three integers and the product of the three integers could be<br>
(1) x, x+1, and x+2  -->  product = (x)(x+1)(x+2) = x^3+3x^2+2x
or
(2) x-1, x, and x+1  -->  product = (x-1)(x)(x+1) = x^3-x
or
(3) x-2, x-1, and x  -->  product = (x-2)(x-1)(x) = x^3-3x^2+2x<br>
Note the simplified forms of the expression for the product indicate that the algebra required to solve a problem involving 3 consecutive integers is often easier if x is used to denote the middle number.<br>
But of course all three options are valid.