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