SOLUTION: Let an integer be represented by x. Find in terms of x the product of the three consecutive integers

Question 1143028: Let an integer be represented by x. Find in terms of x the product of the three consecutive integers
Found 3 solutions by Boreal, Alan3354, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
the integers that are multiplied together are x, x+1 and x+2
The product is x(x^2+3x+2) or x^3+3x^2+2x
check using x=4
product is 4*5*6=120
4^3+3(4^2)+8=120
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Which 3 consecutive integers?
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

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

(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

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.

But of course all three options are valid.
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