Polynomial Calculator — Evaluate ax³ + bx² + cx + d
Quick answer: Enter a, b, c, d, and x to calculate f(x) = ax³ + bx² + cx + d at your chosen x.
Evaluate a cubic polynomial ax³ + bx² + cx + d at any x value. Enter the coefficients and the x to evaluate at, and get the result instantly. Also displays a value table for x = −3 to 3 to understand the polynomial's behavior.
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Last reviewed: April 2026Report an error
Evaluate: f(x) = ax³ + bx² + cx + d at a given x
f(2)
4
f(x) = 1x³ -3x +2. At x = 2: f(2) = 4.
Value Table (x from −3 to 3)
| x=-3 | x=-2 | x=-1 | x=0 | x=1 | x=2 | x=3 |
|---|---|---|---|---|---|---|
| -16 | 0 | 4 | 2 | 0 | 4 | 20 |
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How to Use This Polynomial Calculator Calculator
- 1Enter coefficient a for the x³ term (can be 0 for a lower-degree polynomial).
- 2Enter b for x², c for x, and d for the constant.
- 3Enter the x value to evaluate at.
- 4Read f(x) and the value table.
Frequently Asked Questions
- A polynomial is an expression of the form aₙxⁿ + ... + a₁x + a₀ where the exponents are non-negative integers. Cubic (degree 3) polynomials have at most three roots.
- Substitute x into the expression: f(x) = ax³ + bx² + cx + d. For f(2) with a=1, b=0, c=−3, d=2: f(2) = 8 + 0 − 6 + 2 = 4.
- A root (or zero) is a value of x where f(x) = 0. A cubic polynomial has at most 3 real roots. You can use the value table to spot sign changes, which bracket a root.
- Yes — set a = 0. For bx² + cx + d, enter a=0 and the remaining coefficients.
- Yes — set a = 0 and b = 0. For cx + d, enter a=0, b=0, and the c and d values.
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