Answer:
-11
Step-by-step explanation:
If we call x the least integer, then x + 1 is the next integer, and x + 2 is the greatest integer.
x (x + 1) (x + 2) = -1716
x (x² + 3x + 2) = -1716
x³ + 3x² + 2x = -1716
x³ + 3x² + 2x + 1716 = 0
That's not an easy equation to factor. We could use rational root test, but that would take a long time. However, we can narrow down the options logically. The three integers are relatively close together, so if we approximated the product as x³:
x³ ≈ -1716
x ≈ -11.9
So let's see if x = -12 is a solution:
(-12)³ + 3(-12)² + 2(-12) + 1716 = 396
Nope. Let's try x = -11:
(-11)³ + 3(-11)² + 2(-11) + 1716 = 726
Not that either. Let's go the other direction, x = -13:
(-13)³ + 3(-13)² + 2(-13) + 1716 = 0
Aha! x = -13. So x + 1 = -12, and x + 2 = -11.
-11 × -12 × -13 = -1716
The greatest integer is -11.
