Calculator Form
Example Data Table
| Input Coefficients | Exact Fraction Form | LCM | Scaled Integers | Least Whole Numbers |
|---|---|---|---|---|
| 2/3, -5/6, 1/2, 3 | 2/3, -5/6, 1/2, 3 | 6 | 4, -5, 3, 18 | 4, -5, 3, 18 |
| 0.5, -1.25, 2 | 1/2, -5/4, 2 | 4 | 2, -5, 8 | 2, -5, 8 |
| 3/8, 9/16, -15/32, 1 | 3/8, 9/16, -15/32, 1 | 32 | 12, 18, -15, 32 | 12, 18, -15, 32 |
| -0.75, 1.5, -0.75 | -3/4, 3/2, -3/4 | 4 | -3, 6, -3 | -1, 2, -1 |
Formula Used
Let the input polynomial be P(x) = anxn + an-1xn-1 + ... + a0, where each coefficient may be a fraction or decimal.
First, convert every coefficient into an exact fraction. Next, find the least common multiple of all denominators. Multiply every coefficient by that least common multiple to clear fractions.
After that, find the greatest common divisor of the resulting integers. Divide every scaled integer coefficient by that greatest common divisor. The remaining list is the least equivalent whole-number coefficient set.
In compact form: Whole coefficients = (LCM of denominators × coefficients) ÷ GCD of scaled integers. This keeps the polynomial equivalent up to a nonzero scalar factor.
How to Use This Calculator
- Enter coefficients in descending power order.
- Use integers, decimals, or fractions.
- Choose a variable symbol if needed.
- Set an optional evaluation point.
- Choose graph minimum and maximum x values.
- Select the number of displayed decimal places.
- Keep the leading coefficient positive if you want standard form.
- Press Calculate to show the result above the form.
- Use the CSV or PDF buttons to export the current result.
Why This Calculator Helps
Whole-number coefficients are easier to read, compare, factor, graph, and communicate. When decimals and fractions appear inside a polynomial, algebraic work becomes harder than it needs to be. This tool converts the coefficients into a cleaner integer form while showing the scaling logic behind the transformation.
It is useful in classroom algebra, polynomial modeling, equation cleanup, graph preparation, and answer checking. Because the calculator preserves equivalence up to a nonzero constant multiple, it helps you simplify the presentation without losing the mathematical structure of the expression.
FAQs
1. What does this calculator do?
It converts polynomial coefficients entered as fractions or decimals into the least equivalent whole-number coefficients. It also shows scaling steps, evaluation results, exports, and a graph.
2. Does rescaling change the roots?
No. Multiplying a polynomial by a nonzero constant does not change its roots. It only changes the vertical scaling of the graph.
3. Why is the least common multiple used?
The least common multiple clears all denominators in one step. That creates an integer coefficient list with the smallest shared denominator multiplier.
4. Why divide by the greatest common divisor afterward?
The greatest common divisor removes any remaining common factor from the scaled integers. That produces the smallest equivalent whole-number coefficient set.
5. Can I use decimals and fractions together?
Yes. The parser accepts integers, decimals, and simple fractions in the same coefficient list. Each value is converted into an exact fraction before simplification.
6. What order should the coefficients follow?
Enter them from the highest power down to the constant term. For example, 2, -3, 5 means 2x^2 - 3x + 5.
7. What happens if the first coefficient is negative?
You can keep it negative or force a positive leading coefficient. That option flips every whole-number coefficient by the same sign.
8. What is exported in the CSV and PDF files?
The exports include the exact coefficients, the original polynomial, denominator scaling, reduced whole-number coefficients, derivative, evaluation result, and graph interval summary.