Solve large polynomial expressions using coefficient-driven numeric methods. Inspect derivatives, divisions, roots, and plotted behavior. Download clean reports for study, teaching, and verification tasks.
| Sample Coefficients | Polynomial | x | Derivative Order | Division Value a | Graph Range |
|---|---|---|---|---|---|
| 2, -3, 0, 5, -7, 4 | 2x^5 - 3x^4 + 5x^2 - 7x + 4 | 1.5 | 2 | 1 | -4 to 4 |
| 1, 0, -6, 0, 9 | x^4 - 6x^2 + 9 | 2 | 1 | -3 | -5 to 5 |
| 3, -2, 5, -1, 0, 8, -6 | 3x^6 - 2x^5 + 5x^4 - x^3 + 8x - 6 | -1 | 3 | 2 | -3 to 3 |
Polynomial model: P(x) = anxn + an-1xn-1 + ... + a1x + a0.
Horner evaluation: Start with the leading coefficient, then repeat b = b·x + next coefficient. This reduces repeated powers and improves numeric stability.
Derivative rule: d/dx[akxk] = k·akxk-1. Higher-order derivatives repeat the same transformation until the requested order is reached.
Integral rule: ∫akxkdx = akxk+1 / (k+1) + C. The constant C is user-defined.
Synthetic division: Dividing P(x) by x - a generates a quotient polynomial and remainder. When the remainder is zero, a is a real root.
Root search: The tool scans the chosen interval for sign changes, then refines each bracketed root with bisection for a strong real-root approximation.
It evaluates high-degree polynomials, builds derivatives, forms antiderivatives, performs synthetic division, estimates real roots in a chosen interval, and plots the curve.
Enter numbers from highest degree to constant term. Use commas or spaces. For x^4 - 6x^2 + 9, type 1, 0, -6, 0, 9.
Horner evaluation reduces repeated exponent calculations. It is faster, cleaner, and usually more numerically stable for large-degree polynomial evaluation.
No. The root finder reports real roots suggested by sign changes inside your selected interval. Complex roots and missed repeated roots may not appear.
It divides the polynomial by x - a and returns a quotient plus remainder. A zero remainder confirms that a is a real root.
Yes. Decimal and signed values are accepted. This helps when modeling fitted curves, scaled equations, or normalized algebra problems.
It chooses how many times the polynomial is differentiated. Order 1 gives the first derivative, order 2 gives the second derivative, and so on.
The exports include the displayed result metrics and computed values. They are useful for homework records, solution logs, and review notes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.