I hit upon the following method of calculation during my sophomore year of college when I was working on the representation of algebraic equations.
When I taught this method to first-year students at a senior high school where I was working as a trainee teacher during my senior year of college, they were impressed, and today, this method appears to be widely used.
Let us carry out the following calculations by using this method.
(X - 3)(2X + 1)(X2 + 3X + 1) = ?
(X6 + 4X5 - X4 - 5X3 + 2X2 - 3X - 2)/(X2 - 2X - 2) = ?
Solution
Therefore,
(X - 3)(2X + 1)(X2 + 3X + 1) = 2X4 + X3 - 16X2 - 14X - 3
(X6 + 4X5 - X4 - 5X3 + 2X2 - 3X - 2)/(X2 + 2X - 2)
= X4 + 2X3 - 3X2 + 5X - 14, and the remainder is (35X - 30)
This method can be interpreted as one that involves carry-free addition, subtraction, multiplication, and division.
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