Then the leading coefficient of g does not divide the leading coefficient of f, and the traditional polynomial division algorithm would produce quotients that are not integer-valued.
The division algorithm in hand, one can prove some stronger results:
This is obtained by repeated applications of the division algorithm.
In real life, today, the operation of division is used as a small part of solving a situated problem that begins with the recognition that division is needed; in the '60s, when the context for learning mathematical skills was often in order "to pass the exam or test" an ability to perform the long division algorithm was an achievement in its own right.
There are many methods of computing such an answer and the long division algorithm is but one (and usually the only one we learned at school).
The most popular division algorithm is called a restoring algorithm described in, e.
In each module the increase of the precision (number of remainder bits) was achieved not by the expansion of the dividend width but using the certain number of iterations of the division algorithm.
Section 2 gives the introduction into some standard division algorithms and optimization techniques.
The most frequent error was either the overgeneralisation of a cross-multiplication algorithm or the overgeneralisation of the division algorithm (Benander & Clement, 1985).
The overgeneralisation of the division algorithm stems from the conflict between the visual and the algorithmic approach to fraction operations (Driscoll, 1982)--students are literally unable to see how the algorithm works.
This should be expected because there is no division algorithm for more than two fractions; therefore, overgeneralisation did not occur in this example.
0 uses a proprietary division algorithm
to discover the Pentium flaw.