Polynomial Remainder Theorem Calculator
Easily calculate the remainder when a polynomial is divided by (x-a) using the Polynomial Remainder Theorem. Enter your polynomial and the value of 'a' for instant results.
Enter Polynomial and Value
To find the remainder when P(x) is divided by (x - a), input P(x) and the value of \'a\'.
Calculation Result
Polynomial P(x) entered:
Value of \'a\' entered:
Polynomial P(a) evaluated:
Understanding the Remainder Theorem
The Remainder Theorem states that when a polynomial P(x) is divided by (x - a), the remainder is the value of the polynomial evaluated at x = a, which is P(a).
For the polynomial you entered:
And with a = , we calculated
Thus, the remainder when is divided by (x - ) is:
About Polynomial Remainder Theorem
The Polynomial Remainder Theorem is a fundamental concept in algebra that simplifies finding the remainder of polynomial division. Instead of performing long division, you can directly substitute the value \'a\' into the polynomial P(x) to find the remainder when dividing by (x - a).
Formula: If a polynomial P(x) is divided by (x - a), the remainder R is given by R = P(a).
Example: To find the remainder when P(x) = x² + 3x + 5 is divided by (x - 1), we calculate P(1) = (1)² + 3(1) + 5 = 1 + 3 + 5 = 9. Thus, the remainder is 9.
This tool helps you quickly evaluate polynomials and apply the Remainder Theorem without manual calculations.