The Adding and Subtracting Polynomials Calculator provided by Hesapstan adds or subtracts two single-variable polynomials in x, groups like terms by degree, and writes the final result in descending standard form. For example, (3x² − 2x + 1) + (x² + x − 3) becomes 4x² − x − 2. This tool does not multiply, divide, factor, find roots, handle multivariable expressions, or support fractional exponents such as x^1.5.
Adding or subtracting polynomials means combining like terms
Like terms have the same variable raised to the same power. 3x² and x² can be combined, −2x and x can be combined, and constant terms are combined with other constants.
The calculator parses both polynomials, groups coefficients by degree, adds or subtracts those coefficients, removes zero terms, and then writes the result as a clean polynomial.
Each term of a polynomial consists of a coefficient multiplied by a non-negative integer power of x. In 4x², the coefficient is 4 and the degree is 2. In −2x, the coefficient is −2 and the degree is 1. A constant such as 5 has degree 0. Like terms share the same degree and can be combined by adding or subtracting their coefficients.
This calculator supports single-variable polynomials in x only
Supported terms include x^n, Nx^n, Nx, x, and constant N. Exponents must be non-negative integers, while coefficients may be integers or decimals.
Expressions such as 2xy + 1, x + y, (x+1)(x−2), 1/x, x^1.5, sin(x), log(x), or sqrt(x) are outside the supported runtime scope. The tool is built for adding or subtracting two single-variable polynomials.
Subtraction distributes the negative sign across the second polynomial
When subtraction is selected, the operation is P(x) − Q(x). Every term in Q(x) changes sign before like terms are combined. For example, if P(x)=4x²+3x−1 and Q(x)=x²−2x+5, the subtraction step becomes 4x²+3x−1 − x² + 2x − 5.
A common mistake is changing only the first term after the minus sign. This calculator shows the distribution step so that every term of Q(x) is negated correctly.
Worked example: (4x²+3x−1) − (x²−2x+5)
The following steps show how the calculator processes this subtraction.
- Operation: P(x) − Q(x) = (4x²+3x−1) − (x²−2x+5)
- Distribute the negative sign: 4x²+3x−1 − x² + 2x − 5
- Group x² terms: (4−1)x² = 3x²
- Group x terms: (3+2)x = 5x
- Group constant terms: (−1−5) = −6
- Result in standard form: 3x² + 5x − 6
When subtracting a polynomial from itself, every coefficient cancels to zero. For example, (3x²−2x+1) − (3x²−2x+1) gives x² coefficient 3−3=0, x coefficient −2+2=0, and constant 1−1=0. The result is the zero polynomial, which the calculator displays as 0.
The final answer is written in descending standard form
Standard form lists terms from the highest degree to the lowest degree. In 4x² − x − 2, the x² term comes first, then the x term, then the constant term.
If all terms cancel out, the calculator displays the zero polynomial as 0. This is the expected result when a polynomial is subtracted from itself.
Errors usually mean the input is outside the supported polynomial form
Before parsing terms, the calculator checks for unsupported patterns such as multivariable expressions, parenthesized products, division by a variable, fractional exponents, and math functions. If one is found, it shows an error instead of producing a misleading result.
Clear step-by-step addition and subtraction is a different task from polynomial multiplication, division, factoring, or root finding. This page stays focused on combining like terms accurately.
Frequently Asked Questions
What polynomial forms are supported?
The calculator supports single-variable polynomials in x using terms such as x^n, Nx^n, Nx, x, and constants. Exponents must be non-negative integers.
What are like terms?
Like terms have the same variable and the same exponent. 5x² and −2x² are like terms; 5x² and 5x are not.
Why do signs change when subtracting polynomials?
In P(x) − Q(x), the whole second polynomial is subtracted. That means every term of Q(x) is multiplied by −1 before combining like terms.
What does standard form mean?
Standard form writes the polynomial in descending powers: highest degree first, then lower degrees, then the constant term.
Can I add polynomials with multiple variables?
No. This calculator supports x only. Expressions such as 2xy + 1 or x + y are not supported.
Does this calculator factor or multiply polynomials?
No. It only adds or subtracts two polynomials. Multiplication, division, factoring, and root finding are outside this page's scope.
What is the zero polynomial?
The zero polynomial is the result 0, which appears when every term cancels out, such as P(x) − P(x).