Solve binomial polynomial division from coefficients or roots. Review long-division logic, remainder checks, and downloads. Build confidence through examples, verification, responsive inputs, and plotting.
| Dividend | Divisor | Quotient | Remainder |
|---|---|---|---|
| x3 - 6x2 + 11x - 6 | x - 2 | x2 - 4x + 3 | 0 |
| 2x2 + 5x + 3 | x + 2 | 2x + 1 | 1 |
| 2x3 + 7x2 + 3x + 4 | 2x + 1 | x2 + 3x | 4 |
| 4x2 - x + 9 | x - 3 | 4x + 11 | 42 |
If P(x) is the dividend and ux + v is the binomial divisor, then the division identity is:
P(x) = (ux + v)Q(x) + r
For a dividend anxn + ... + a0, the quotient coefficients are found from highest degree downward.
qn-1 = an / uqn-2 = (an-1 - vqn-1) / ur = a0 - vq0When the divisor is x - c, the remainder theorem gives r = P(c). For ux + v, the divisor root is -v/u, so the remainder is P(-v/u).
ax + b using the two divisor inputs.This page handles classic polynomial division by a linear binomial using a coefficient-first workflow. That makes classroom checks faster because you can test examples directly from factor form, long-division practice sheets, and symbolic algebra homework. The result panel confirms the quotient and remainder, then rebuilds the dividend to verify the identity.
The step table shows how each leading coefficient produces a quotient coefficient. It also records how the divisor constant transfers into the next term. That is useful when a remainder appears unexpectedly, because you can inspect exactly where the next coefficient changed and compare the process against hand-written long division.
The graph adds a visual layer. You can compare the dividend, divisor, and quotient over a chosen interval, which is helpful when studying roots, sign changes, or large-output behavior. Although the quotient does not replace the dividend graphically, plotting all three functions side by side supports pattern recognition and error detection.
Exports keep a clean record for lessons, worksheets, and revision notes. CSV files are practical for tabular archiving, while the PDF summary is better for printing or sharing. Together, the calculator supports numeric input, symbolic interpretation, identity verification, and a structured workflow for binomial polynomial division.
Enter coefficients from the highest degree term down to the constant. Separate them with commas. For x³ - 6x² + 11x - 6, enter 1, -6, 11, -6.
Set the divisor x coefficient to 1 and the constant to -4. The calculator interprets those values as x - 4 and performs the division accordingly.
Yes. Enter 2 for the x coefficient and 3 for the constant. The solver divides by the full linear binomial, not only monic divisors.
The remainder is the constant left after division is complete. It tells you how far the dividend is from being exactly divisible by the chosen binomial divisor.
The divisor root is the x value that makes the divisor equal zero. It is useful for checking the remainder theorem and confirming the division result.
The quotient becomes zero and the dividend itself becomes the remainder. The calculator reports that case automatically and skips unnecessary division steps.
No. The graph is a visual aid. The formal confirmation comes from the identity P(x) = divisor × quotient + remainder and the reconstruction check.
Use CSV when you want a structured table for spreadsheets or records. Use PDF when you want a printable summary for assignments, revision, or sharing.
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.