Polynomial Factor Theorem Checker: Is (x-a) a Factor?
Check if (x-a) is a factor of a polynomial instantly with our free online Factor Theorem Checker. Enter your polynomial and 'a' value for quick results and easy algebra.
Use '^' for exponents (e.g., x^2). Ensure valid mathematical syntax.
Value of \(a\) in the factor \((x - a)\).
Factor Theorem Result
Understanding Factor Theorem
The Factor Theorem states that for a polynomial \({p(x)}\), \((x - a)\) is a factor of \({p(x)}\) if and only if \({p(a) = 0}\).
Factor Theorem:
$$ p(a) = 0 \iff (x-a) \text{ is a factor of } p(x) $$
We substitute \(x = a\) into the polynomial \({p(x)}\), where \(a = \) .
If the result \({p(a)}\) is \(0\), then \((x - \)\()\) is a factor. Otherwise, it is not.
Since \(p(\)\() = 0\), \((x - \)\()\) is a factor of the polynomial.
Since \(p(\)\() \neq 0\), \((x - \)\()\) is not a factor of the polynomial.
About the Factor Theorem
The Factor Theorem is a key concept in algebra that links the roots of a polynomial to its factors. It's particularly useful for quickly checking if a linear expression \((x - a)\) divides a polynomial \({p(x)}\) without performing long division.
To use this tool, simply input your polynomial and the value of \(a\). The tool will evaluate \({p(a)}\) and determine if it equals zero. If it does, then \((x - a)\) is a factor; otherwise, it is not. This method is much faster than polynomial long division, especially for higher-degree polynomials.
How to Use:
- Enter your polynomial in the 'Polynomial' field. Use standard mathematical notation (e.g.,
x^3 + 2x^2 - 5x + 6). - Enter the value of \'a\' in the 'Value of a' field. This corresponds to the \(a\) in the factor \((x - a)\).
- Click 'Check Factor' to see if \((x - a)\) is a factor.
- View the result below, indicating whether \((x - a)\) is a factor. Copy the result if needed.
Learn more about the Factor Theorem on Wikipedia.