11 is added to a certain number, the sum is multiplied by 7, the product is divided by 6 and finally 2 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number?

A division algorithm is a rule that calculates the quotient and remainder of two integers, N and D, using Euclidean division. It can be applied by hand or used in software and digital circuit designs.  The division algorithm states that for any integer, a, and any positive integer, b, there are unique integers q and r such that a = bq + r. In this equation, r is greater than or equal to 0 and less than b.  The division algorithm can also be applied to polynomials.  The division algorithm for polynomials states that:  f(x) = q(x) g(x) + r(x)  This is the same as:  Dividend = Divisor *... Show more

A division algorithm is a rule that calculates the quotient and remainder of two integers, N and D, using Euclidean division. It can be applied by hand or used in software and digital circuit designs. 

The division algorithm states that for any integer, a, and any positive integer, b, there are unique integers q and r such that a = bq + r. In this equation, r is greater than or equal to 0 and less than b. 
The division algorithm can also be applied to polynomials. 

The division algorithm for polynomials states that: 
f(x) = q(x) g(x) + r(x) 
This is the same as:  Dividend = Divisor * Quotient + Remainder 

Here, r(x) is the remainder polynomial and is equal to 0 and degree r(x) < degree g(x). 
For example, the division algorithm can be used to find the other two zeros of a polynomial if one of the zeros is known.

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