Polynomial Basics
Degree = highest power with non-zero coefficient
Example: 2x³ − 5x² + 3x − 7 (degree 3, 4 terms)
Polynomial Terminology
| Term | Meaning | Example |
|---|---|---|
| Monomial | One term | 4x² |
| Binomial | Two terms | x² − 9 |
| Trinomial | Three terms | x² + 5x + 6 |
| Degree | Highest exponent | x³ → degree 3 |
| Leading coefficient | Coefficient of highest term | 3 in 3x⁴+... |
| Constant term | Term with no x | −7 in 2x²−7 |
Frequently Asked Questions
How do I multiply two polynomials?
Use the distributive property: multiply every term of the first polynomial by every term of the second, then collect like terms. For (x+2)(x+3): x·x + x·3 + 2·x + 2·3 = x² + 3x + 2x + 6 = x² + 5x + 6. This calculator does this automatically for up to degree 5 polynomials.
What is the Remainder Theorem?
When a polynomial P(x) is divided by (x − a), the remainder equals P(a). So evaluating a polynomial at x = a (which this calculator does) is equivalent to finding the remainder of P(x) ÷ (x − a). If P(a) = 0, then (x − a) is a factor.
How do I find roots of a polynomial?
Roots are values of x where P(x) = 0. For degree 1: solve ax + b = 0. For degree 2: use the quadratic formula. For degree 3–4: use Cardano/Ferrari formulas or numerical methods. For degree 5+: no general algebraic formula exists (Abel–Ruffini theorem) — numerical methods like Newton's method are used.