The product of three consecutive integers is 720. What is the polynomial that represent the product?
n(n+1)(n+2)
To find the polynomial that represents the product of three consecutive integers, we can set up an equation based on the given information.
Let's assume the first integer is x. Since the integers are consecutive, the second integer would be x + 1, and the third integer would be x + 2.
The product of these three consecutive integers is given by:
(x) * (x + 1) * (x + 2)
To simplify the expression further, we can expand it:
(x^2 + x) * (x + 2)
= (x^2 + x) * x + (x^2 + x) * 2
= x^3 + 2x^2 + x^2 + 2x
= x^3 + 3x^2 + 2x^2 + 2x
= x^3 + 5x^2 + 2x
Therefore, the polynomial that represents the product of the three consecutive integers is:
P(x) = x^3 + 5x^2 + 2x