Factor Theorem Calculator
Test if (x - c) is a factor of a polynomial using the Factor Theorem.
Enter Polynomial
For x³ - 6x² + 11x - 6, enter: 1, -6, 11, -6
Tests if (x - c) is a factor for each value c
Factor Theorem
(x - c) is a factor of P(x) if and only if P(c) = 0.
Results
P(x) =
x^3 - 6x^2 + 11x - 6
Factors Found
(x - 1) × (x - 2) × (x - 3)
P(1) = 0Factor!
(x - 1) is a factor of P(x)
P(2) = 0Factor!
(x - 2) is a factor of P(x)
P(3) = 0Factor!
(x - 3) is a factor of P(x)
Understanding the Factor Theorem
The Theorem
For a polynomial P(x), (x - c) is a factor of P(x) if and only if P(c) = 0. This is a special case of the Remainder Theorem where the remainder is zero.
Example
P(x) = x³ - 6x² + 11x - 6
P(1) = 1 - 6 + 11 - 6 = 0
Since P(1) = 0, (x - 1) is a factor