Question

The product of three integers x, x+2, and x-5 is 240. What are the integers?

Answer 1

8, 10, 3

Explanation:

For finding real solutions to cubic equations and those of higher degree, I find a graphing calculator to be useful. The problem can be cast in the form ...

f(x) = 0

where f(x) is the difference between the product of the integers and 240:

f(x) = x(x +2)(x -5) -240

Then all we need to do is ask the calculator to show the x-intercept. It is x=8.

So, the three integers are ...

• x = 8
• x+2 = 10
• x -5 = 3