Polynomial Remainder Theorem Proof Calculator

Calculate P(a) and Verify the Remainder Theorem

Enter coefficients from highest degree to constant term, separated by commas. For missing terms, use 0.
E.g., for 3x^3 + 2x - 5, enter 3, 0, 2, -5

Explore and verify the Polynomial Remainder Theorem effortlessly. This tool helps you understand that for a polynomial P(x), the remainder of division by a linear factor (x-a) is simply P(a). Input your polynomial's coefficients and the value 'a' to see this fundamental algebraic principle in action.

Formula:

The Polynomial Remainder Theorem states that if a polynomial P(x) is divided by a linear factor (x - a), then the remainder is R = P(a).

Where:

  • P(x): The polynomial (e.g., 3x2 + 2x - 5)
  • (x - a): The linear divisor (e.g., x - 2, so a = 2)
  • P(a): The value of the polynomial when x = a
  • R: The remainder of the polynomial division

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