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Remainder Theorem

Dividing f(x) by x - c leaves a remainder of exactly f(c).

The Remainder Theorem: for a polynomial f and any number c, dividing f(x) by x - c leaves a remainder equal to f(c). So evaluating a polynomial and dividing it by a linear factor are, secretly, the same computation.

Examples

  • Dividing f(x) = x^2 + 3x - 4 by x - 1 leaves remainder f(1) = 0.

See also

synthetic division Factor Theorem
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