424 Cubic Equations in Real Numbers
To set up the synthetic division “grid,” we write down the coefficients and the stand-
alone constant in an array along with “wildcard” entries symbolized by pound signs (#),
like this:# abcd
###
####In our example, we have a= 1, b= 0, c=−7, and d=−6. We put those numbers into the top
row from left to right, starting immediately to the right of the pound sign:#10− 7 − 6
###
####Now the guessing game begins! At first, we have no clue as to what the real root might be. Let’s
try 2 as a “test root.” We put that number in the top left slot:(^210) − 7 − 6
Next, we copy the second number in the top row to the “wildcard” slot directly beneath it in
the bottom row:
(^210) − 7 − 6
1###
We multiply 2 by 1 and place the product in place of the first wildcard in the second row:
(^210) − 7 − 6
2##
1###
We add the numbers in the third column, writing the sum in the bottom row:
(^210) − 7 − 6
2##
12##