SOLUTION: Find 3 consecutive whole numbers with a product of 720

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Question 923800: Find 3 consecutive whole numbers with a product of 720
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x%28x%2B1%29%28x%2B2%29=720
x%28x%5E2%2B3x%2B2%29=720
x%5E3%2B3x%5E2%2B2x-720=0

Use synthetic division for Rational Roots Theorem and examine only the positive possible roots. You are also only interested in the possible roots less than 180 (just a guess).

I found only this:

_______8______|_______1______3_______2_______-720
______________|
______________|
______________|_____________8_______88_______720
______________|________________________________________
_____________________1______11_______90________0


One of the binomial factors is highlight%28x-8%29 for a root of 8. This is the only rational root found (used a graph to check).

Your three whole numbers are 8, 9, 10.