Add and Subtract Polynomials Calculator
Align matching powers. Distribute every sign. See your result take shape.
Build your polynomials
Up to degree 2POLYNOMIAL 1 · P₁(x)
POLYNOMIAL 2 · P₂(x)
The minus sign changes every term in P₂, including negative terms.
Finite decimals and scientific notation · up to 60 significant digits per coefficient; exponent −100 to 100.
Like terms combined · written in descending powers.
Full exact result
Three curves. One operation.
Pointwise difference
Distribute. Group. Simplify.
Step by stepAlign matching powers
Coefficient balance| Power | P₁ | P₂ | Difference |
|---|---|---|---|
| x² | 1 | 0 | 1 − 0 = 1 |
| x | 2 | 1 | 2 − 1 = 1 |
| Constant | 3 | 1 | 3 − 1 = 2 |
P₂ has no x² term, so its x² coefficient is 0.
Only terms with the same variable and exponent can be combined.
= +3x − 2
A minus sign belongs to every term.
Subtracting a negative coefficient becomes addition. Flip each sign first, then combine matching powers.
Formula & interpretation
= (a₁ ± a₂)x² + (b₁ ± b₂)x + (c₁ ± c₂)
Add or subtract corresponding coefficients. Keep each power of x unchanged, then remove zero terms.
When leading terms cancel, the result may be linear, constant, or the zero polynomial.
Frequently asked questions
Why write x instead of 1x?
A coefficient of 1 is omitted on variable terms. A coefficient of −1 is written as a minus sign.
What is the degree of the zero polynomial?
Its degree is undefined under the standard elementary convention. A nonzero constant has degree 0.
Why do signs change during subtraction?
Subtracting a polynomial multiplies every term of that polynomial by −1.
Does this builder accept higher-degree polynomials?
This coefficient builder supports degree 2 and below. The same like-term rules apply to higher degrees.
Sources & Reference Guides
Independent educational reference · No institutional endorsement or expert review claimed.
Align matching powers. Distribute every sign. See your result take shape.