Add and Subtract Polynomials Calculator
The Add and Subtract Polynomials Calculator combines two quadratic polynomials of the form ax² + bx + c by adding or subtracting like terms. Enter the coefficients of each polynomial, choose the operation, and it returns the resulting polynomial with its coefficients collected.
Formula
(a₂x² + a₁x + a₀) ± (b₂x² + b₁x + b₀) = (a₂±b₂)x² + (a₁±b₁)x + (a₀±b₀)
- To add or subtract polynomials, combine the coefficients of like terms — x² with x², x with x, and constants with constants.
- Subtraction flips the sign of every term in the second polynomial before combining.
- This calculator works with quadratics; set a coefficient to 0 for lower-degree polynomials (for example, a2 = 0 gives a linear expression).
- Terms with a zero coefficient are omitted from the displayed result.
Example Calculation
Inputs
- First polynomial — x² coefficient: 1
- First polynomial — x coefficient: 2
- First polynomial — constant: 3
- Operation: add
- Second polynomial — x² coefficient: 0
- Second polynomial — x coefficient: 1
- Second polynomial — constant: 1
(x² + 2x + 3) + (x + 1): add like terms to get x² + 3x + 4.
Frequently asked questions
How do you add polynomials?
Add the coefficients of matching terms: the x² terms together, the x terms together, and the constants together.
How does subtraction work?
Subtracting a polynomial means changing the sign of each of its terms and then adding, which this calculator does automatically.
Can I use it for linear expressions?
Yes. Set the x² coefficients to 0 and the calculator handles linear (or constant) expressions.
Why are some terms missing from the answer?
Terms whose coefficient works out to zero are left out, so 0x² + 3x + 4 is shown simply as 3x + 4.
What about higher-degree polynomials?
This tool covers up to quadratics. For higher degrees, apply the same like-terms rule to each power of x.