P(x) Polynomial Calculator
Evaluate a polynomial at a given x, or add and subtract two polynomials. Enter coefficients as comma-separated values from the highest degree term to the constant.
Enter coefficients from highest degree to constant. E.g. 2, -3, 1 = 2x² − 3x + 1
Term-by-term breakdown:
Polynomial Formulas
Worked Examples
Example 1 — Evaluate P(3) for 2x² − 3x + 1
Example 2 — Add (3x² − 2x + 1) + (x² + 4x − 5)
Result: 4x² + 2x − 4
Frequently Asked Questions
A polynomial is an expression consisting of variables and coefficients, involving operations of addition, subtraction, and non-negative integer exponents. Examples: 3x² − 2x + 5 (quadratic), x³ + 1 (cubic). Polynomials do not include division by a variable or fractional exponents.
Substitute the given value of x into the polynomial and compute each term. For P(x) = 2x² − 3x + 1 at x = 4: P(4) = 2(16) − 3(4) + 1 = 32 − 12 + 1 = 21. Use Horner's method for efficiency with high-degree polynomials.
The degree is the highest exponent of the variable in the polynomial. For 4x³ − 2x + 7, the degree is 3. The degree determines many properties: a degree-n polynomial can have at most n real roots and its graph can change direction at most n−1 times.
Align like terms (same power of x) and add their coefficients. For (3x² + 2x − 1) + (x² − 5x + 4): x² terms: 3+1=4, x terms: 2+(−5)=−3, constants: −1+4=3. Result: 4x² − 3x + 3.
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