Remainder theorem calculator

Find the remainder when dividing a polynomial by (x − c) using the remainder theorem: f(c) = remainder.

Polynomial
Divisor

Remainder theorem

When polynomial f(x) is divided by (x − c), the remainder equals f(c).

If f(c) = 0, then (x − c) is a factor of f(x), and c is a root.

Example

f(x) = x³ − 6x² + 11x − 6, divided by (x − 2):

f(2) = 8 − 24 + 22 − 6 = 0. So (x − 2) is a factor and x = 2 is a root.

Factor theorem

The factor theorem is a special case: (x − c) is a factor of f(x) if and only if f(c) = 0.

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