Calculator Form
Enter a constant multiplier and up to three linear factors of the form (ax + b). Only the first selected factors are used.
Formula Used
General Linear Factor Form
k(a₁x + b₁)(a₂x + b₂)(a₃x + b₃) is expanded by polynomial multiplication. Each multiplication combines coefficients term by term.
Two-Factor Expansion
(ax + b)(cx + d) = acx² + (ad + bc)x + bd
Three-Factor Expansion
(ax + b)(cx + d)(ex + f) becomes a cubic after coefficient convolution. The calculator performs this automatically and lists every resulting coefficient.
Root from One Linear Factor
For a factor (ax + b), the root is x = -b / a, when a ≠ 0.
How to Use This Calculator
- Select how many factors you want to expand.
- Enter the constant multiplier k.
- Fill the coefficients for each factor in the form (ax + b).
- Set the graph range and step size.
- Press Expand Factors to see the expanded expression.
- Review the steps, coefficient table, value table, and graph.
- Download the result data in CSV or PDF format.
Example Data Table
Example expression: (x + 2)(x - 3)
| Factored Form | Expanded Form | Degree | Coefficient of x² | Coefficient of x | Constant |
|---|---|---|---|---|---|
| (x + 2)(x - 3) | x² - x - 6 | 2 | 1 | -1 | -6 |
| 2(x + 1)(x + 4) | 2x² + 10x + 8 | 2 | 2 | 10 | 8 |
| (2x - 1)(x + 5) | 2x² + 9x - 5 | 2 | 2 | 9 | -5 |
| (x + 1)(x + 2)(x + 3) | x³ + 6x² + 11x + 6 | 3 | 1 | 11 | 6 |
FAQs
1. What does this factor expansion calculator do?
It expands one, two, or three linear factors into a simplified polynomial. It also shows steps, coefficients, roots from factors, value tables, and a graph.
2. What type of factors can I enter?
You can enter linear factors in the form (ax + b). The calculator supports a constant multiplier and up to three such factors in one expression.
3. Can this calculator handle cubic expansions?
Yes. When you choose three linear factors, the final expanded expression can become a cubic polynomial, depending on the entered coefficients.
4. Why are roots shown in the result?
Each linear factor gives a root using x = -b/a. These roots help you connect the factored form to the graph and understand where the expression becomes zero.
5. What is the benefit of the coefficient table?
The coefficient table separates each term clearly. This makes checking polynomial structure easier, especially for homework, teaching, verification, and pattern recognition.
6. What does the Plotly graph show?
It plots the expanded polynomial over your chosen x-range. This helps you see turning behavior, sign changes, intercepts, and overall curve shape more clearly.
7. Can I download the calculation results?
Yes. After calculating, you can export a CSV file for spreadsheet use or a PDF file for printing, sharing, or saving your work.
8. Is this calculator useful for learning algebra?
Yes. It is useful for practice because it connects factor form, expanded form, coefficient patterns, roots, tables, and graphs in one place.