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
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.
