Factor Theorem Calculator
Test whether x-r is a factor of a polynomial by evaluating P(r).
Calculator
What this calculator teaches
The Factor Theorem connects roots and factors. If r is a root, then x-r is a factor.
This calculator is a fast way to check factor candidates from the Rational Root Theorem.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Factor theorem | P(r)=0 ⇔ (x-r) is a factor | A zero value means the binomial divides the polynomial exactly. |
| Remainder theorem | remainder=P(r) | The value P(r) is the remainder after division by x-r. |
Step-by-Step Examples
- Use r=1.
- P(1)=1-3+2.
- P(1)=0.
Where students use this
Common Mistakes to Avoid
Mathematical notation is compact, but calculators need explicit numbers and operators.
Some formulas only work when denominators are nonzero, logs have positive inputs, and square roots are valid.
Keep extra decimals while solving and round only the final answer.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.