Polynomial Division & Remainder Theorem

$P(x) = ax^n + bx^{n-1} + \dots$

Understanding Polynomial Operations

Polynomials are expressions consisting of variables (also called indeterminates) and coefficients, that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. This explorer helps you with key polynomial concepts and operations:

Remainder Theorem: Quickly find the remainder when a polynomial $P(x)$ is divided by $(x-c)$.
Factor Theorem: Determine if $(x-c)$ is a factor of $P(x)$.
Polynomial Long Division: Perform step-by-step division of one polynomial by another.

Enter polynomials using 'x' as the variable, e.g., x^3 - 2x^2 + x - 5. Use ^ for exponents (e.g., x^2 for $x^2$). Ensure spaces around operators like + and - for robust parsing, e.g., x^2 - 4 rather than x^2-4.

Remainder Theorem Solver

The Remainder Theorem states: If a polynomial $P(x)$ is divided by a linear binomial $(x-c)$, the remainder is $P(c)$.

$P(x)$ (Polynomial):

$c$ (Value from $x-c$):

Factor Theorem Tester

The Factor Theorem states: A polynomial $P(x)$ has a factor $(x-c)$ if and only if $P(c) = 0$.

$P(x)$ (Polynomial):

$c$ (Value from $x-c$ to test as a root):

Polynomial Long Division

Divides a polynomial (dividend) by another (divisor) to find the quotient and remainder.

Dividend $P(x)$:

Divisor $D(x)$: