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

  8, 10, 3

Step-by-step 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 ...

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.