# Adding and Subtracting Polynomials Calculator

URL: https://speedycalculator.com/calculators/math/add-subtract-polynomials/
Last updated: 2026-10-30

> The adding and subtracting polynomials calculator combines two polynomials of degree up to 6 by adding or subtracting the coefficients of like powers of x.

## Inputs

- I want to…
- Degree of P(x)
- a₆ (x⁶)
- a₅ (x⁵)
- a₄ (x⁴)
- a₃ (x³)
- a₂ (x²)
- a₁ (x)
- a₀
- Degree of Q(x)
- b₆ (x⁶)
- b₅ (x⁵)
- b₄ (x⁴)
- b₃ (x³)
- b₂ (x²)
- b₁ (x)
- b₀

## Results

- Result
- P(x)
- Q(x)
- Degree of the result

## Formula

```
P(x) ± Q(x): coefficient of xⁱ = aᵢ ± bᵢ
```

## Explanation

Adding polynomials is collecting like terms: x² terms with x² terms, x terms with x terms and constants with constants. Subtracting is the same, except every coefficient of the second polynomial changes sign first – the step where most mistakes happen.

### How to use the Adding and Subtracting Polynomials Calculator

- Choose the **degree** of each polynomial – the matching coefficient fields appear.
- Enter the **coefficients** from the highest power down; leave a field at 0 for a missing power.
- Read the result, written with powers of x in descending order.

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The calculator lines up the coefficients by power and adds or subtracts them, then removes leading zero terms so the degree of the result is correct.

## Worked example

Inputs — I want to…: Add: P(x) + Q(x); Degree of P(x): 3; a₃ (x³): 3; a₂ (x²): -2; a₁ (x): 0; a₀: 5; Degree of Q(x): 2; b₂ (x²): 1; b₁ (x): 4; b₀: -7.

Results — **Result = 3x³ − x² + 4x − 2**; P(x) = 3x³ − 2x² + 5; Q(x) = x² + 4x − 7; Degree of the result = 3.

## Key terms

- **Like terms**: Terms with the same variable raised to the same power.
- **Degree**: The highest power of x with a non-zero coefficient.

## FAQ

**How do I subtract polynomials?**
Change the sign of every term of the second polynomial and add: (3x² + 2) − (x² − 5) = 2x² + 7.

**What are like terms?**
Terms with the same power of x, such as 4x³ and −x³.

**Can the degree go down?**
Yes – if the leading terms cancel, for example (x² + 1) − (x² − 3) = 4.

**Does the order matter?**
For addition no; for subtraction P − Q = −(Q − P).


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Intermediate Algebra 2e](https://openstax.org/details/books/intermediate-algebra-2e)