Enter a polynomial expression to convert it to standard form. The calculator expands parentheses, combines like terms, and orders terms by descending degree.
Standard Form: x³ + 3x² − 5x − 5
Degree: 3
Leading Coefficient: 1
Note: Use 'x' as the variable, '^' for exponents (e.g., x^3), and standard operators +, -, *, /.
What is the Standard Form of a Polynomial?
A polynomial is in standard form when its terms are arranged in descending order of degree — from the highest exponent to the lowest [citation:12]. The general form of a polynomial in standard form with a single variable x is:
anxn + an−1xn−1 + ... + a1x + a0
Where:
- an, ..., a0 — coefficients (real numbers)
- x — the variable
- n — the degree of the polynomial (highest exponent)
To convert a polynomial to standard form, you must:
- Expand parentheses — remove brackets by applying the distributive property [citation:1]
- Combine like terms — add coefficients of terms with the same variable and exponent [citation:4]
- Order terms — arrange from highest to lowest degree [citation:12]
For example, the polynomial 3x² + 2x − 5 + x³ − 7x can be simplified to x³ + 3x² − 5x − 5. The term with the highest degree (x³) comes first, followed by the next highest (3x²), and so on [citation:12].
Standard form makes polynomials easier to read, compare, and analyze. It is essential for solving polynomial equations, graphing functions, and many other algebraic operations [citation:3].
How to Use This Calculator
- Enter a polynomial: Type or paste your polynomial expression in the text area. Use ‘x’ for the variable, ‘^’ for exponents (e.g., x^3), and standard operators: +, -, *, /.
- Examples:
3x^2 + 2x - 5 + x^3 - 7x,2x * (x + 3) - 4, orx^4 - 2x^2 + 1. - Calculate: Click the “Convert to Standard Form” button or press Enter.
- Reset: Use the “Reset” button to restore the default example.
- Interpretation: The result shows the polynomial in standard form, its degree, and the leading coefficient. For example,
x³ + 3x² − 5x − 5has degree 3 and leading coefficient 1.