if you add the coefficients then why does the 8 plus 2 become 10 then on your remainder a negative 10??   i thought you add them  

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Hi James, thanks for you question.  The 8 and 2 do become 10.  But then we multiply that number by -1 (the number in the box on the upper left).  The result is -10.  The numbers in the second row, -1, 2, and -10, are what you get when you multiply each number in the bottom row (1, -2, and 10) by that -1 in the upper left box.  The remainder, 10 + (-10) = 0, goes in the lower right box.  A zero remainder tells us that -1 is indeed a zero of our polynomial.