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Polynomial Calculator
Perform polynomial arithmetic (addition, subtraction, and multiplication) up to degree 3 or evaluate a single polynomial at a given value of x with step-by-step synthetic substitution.
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Interactive Polynomial Calculator Workspace
Polynomial P(x) Coefficients
Expression: 2x³ -1x² + 3x + 4
Polynomial Q(x) Coefficients
Operation:
Expression: 3x² -2x + 5
Calculated Output Polynomial2x³ + 2x² + 1x + 9
Simplifying Steps
Polynomial P(x) = 2x³ -1x² + 3x + 4
Polynomial Q(x) = 3x² -2x + 5
Calculate P(x) + Q(x) by grouping like-degree terms:
x³ terms: (2) + (0) = 2
x² terms: (-1) + (3) = 2
x¹ terms: (3) + (-2) = 1
Constant terms: (4) + (5) = 9
Mathematical Formula & Variables
Equation Model
P(x) = anxⁿ + ... + a₁x + a₀ | P(x) + Q(x) = ∑ (ai + bi)xⁱPolynomial addition/subtraction aggregates like-degree terms. Multiplication distributes every term of the first polynomial into every term of the second. Evaluation replaces variable instances with the specific x value.
Variable Definitions
| Symbol | Description |
|---|---|
| P(x), Q(x) | The polynomials expressed as series of coefficients |
| x | The scalar value utilized during substitution evaluation |
How to Use the Polynomial Calculator
- Choose the operational tab: "Add/Subtract", "Multiply", or "Evaluate".
- Input the coefficients of your polynomials (constant up to degree 3).
- For evaluation, provide the target numerical value of x.
- Click calculate to see the simplified polynomial expression or the final evaluated result.
Practical Example Calculation
Scenario Context: Evaluating the polynomial P(x) = 2x³ - 3x + 4 at x = 2.
Step 1: Substitute x = 2 into P(x): 2(2)³ - 3(2) + 4.
Step 2: Compute the cubic term: 2 × 8 = 16.
Step 3: Compute the linear term: -3 × 2 = -6.
Step 4: Add constant term: 16 - 6 + 4 = 14.
P(2) is equal to 14.
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