Enter two polynomials into First Polynomial and Second Polynomial, choose Addition or Subtraction, and get the simplified result with like terms combined. Supports standard polynomial notation like 3x^2 + 2x - 5 — perfect for checking algebra homework or verifying manual calculations.
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A polynomial is a mathematical expression made up of variables (like x), coefficients, and exponents, combined using addition, subtraction, or multiplication. Examples include 3x^2 + 2x - 5 (trinomial) or 4x + 7 (binomial). Polynomials do not include division by a variable or fractional exponents.
To add two polynomials, identify and combine like terms — terms that share the same variable and exponent. For example, (3x^2 + 2x + 4) + (2x^2 + x + 1) = (3+2)x^2 + (2+1)x + (4+1) = 5x^2 + 3x + 5. Simply add the coefficients of matching powers.
To subtract polynomials, distribute the negative sign to all terms in the second polynomial, then combine like terms. For example, (3x^2 + 2x + 4) − (2x^2 + x + 1) = 3x^2 + 2x + 4 − 2x^2 − x − 1 = x^2 + x + 3. The key step is changing the sign of every term in the polynomial being subtracted.
When adding polynomials, you simply combine like terms by summing their coefficients. When subtracting, you first negate all terms in the second polynomial (flip their signs) and then combine like terms. The process is the same after that initial sign change.
Like terms are terms that have the same variable raised to the same power. For instance, 4x^2 and -7x^2 are like terms (both have x squared), but 4x^2 and 4x are not like terms. Only like terms can be combined during addition or subtraction.
Type your polynomial using standard notation: use ^ for exponents (e.g. x^2 for x squared), use * or just juxtapose for multiplication (e.g. 3x^2), and use + or - to separate terms. For example, enter 3x^2 + 2x - 5 or 4x^3 - x + 8. The calculator handles single-variable polynomials in x.
The degree of a polynomial is the highest exponent (power) among all its terms. For example, 5x^3 + 2x - 1 has degree 3. When adding or subtracting polynomials, the degree of the result is at most the highest degree of the two input polynomials (it may be lower if leading terms cancel).
Yes, absolutely. Polynomials can have negative, positive, or zero coefficients. A term like -4x^2 simply means the coefficient of x^2 is -4. The calculator handles negative coefficients correctly — just write them with a minus sign (e.g. -4x^2 + 3x - 7).