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.
Formula
P(x) ± Q(x): coefficient of xⁱ = aᵢ ± bᵢ
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.
Frequently asked questions
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).