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what is the difference between a factor theorem and a remainder theorem?
The remainder theorem is a shortcut way of finding the remainder when a polynomial is divided by (x - a). In the polynomial substitute "a" for "x" and evaluate. The result is the remainder. This saves you the effort of doing synthetic division (or long division).

The factor theorem is similar to the remainder theorem. The difference is that after you substitute "a" for "x"; if the result is 0, then (x-a) is a factor of the polynomial and "x=a" is a solution to the equation: polynomial = 0.


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