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Polynomial Addition and Subtraction Calculator

Add or subtract polynomials by combining like powers

First polynomial coefficients
Second polynomial coefficients
Operation

Polynomial Addition and Subtraction Formula

(aₙxⁿ+...+a₀) ± (bₙxⁿ+...+b₀) = (aₙ±bₙ)xⁿ+...+(a₀±b₀)

Polynomial addition and subtraction align terms with the same exponent, then combine their coefficients. Powers stay unchanged; only coefficients change. For subtraction, distribute the minus sign before simplifying.

Note: Use 0 for missing middle terms when entering coefficients, especially for sparse polynomials like x³+2.

How Polynomial Combining Works

Handle each power of x separately, combining only terms that share the same exponent.

Align Powers

Write both polynomials so matching exponents are in the same column.

Add Coefficients

For addition, combine same-power coefficients directly.

Distribute Minus

For subtraction, change signs in the second polynomial first.

Simplify Zeros

Terms with coefficient 0 disappear from the final polynomial.

💡 Example: (3x³-2x+5)+(x²+4x-6)=3x³+x²+2x-1.

Applications of Polynomial Addition and Subtraction

Expression SimplificationFunction OperationsAlgebra HomeworkPolynomial Models

Frequently Asked Questions

What is a polynomial addition and subtraction calculator?
It adds or subtracts two polynomials by aligning like powers and combining their coefficients.
How do I enter polynomials?
Enter coefficients from highest degree to constant term, separated by commas. Use 0 for missing powers.
How do you add polynomials?
Add coefficients of matching powers, such as x² terms with x² terms and constants with constants.
How do you subtract polynomials?
Distribute the minus sign to the second polynomial, then combine like terms.
Why align powers before combining?
Only like terms with the same variable and exponent can be added or subtracted directly.

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