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Remainder Theorem


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The following result about polynomials:

Theorem

If a polynomial f(x) is divided by xh, then the remainder is equal to f(h).

It is proved as follows. Divide the polynomial f(x) by xh to get a quotient q(x) and a remainder which will be a constant, r. This means that f(x)=(xh)q(x)+r. Replacing x by h in this equation gives r=f(h), thus proving the theorem. An important consequence of the Remainder Theorem is the Factor Theorem.

Subjects: Mathematics.


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