Add or subtract two polynomials with up to 4 terms each. See the combined result, degree, leading coefficient, step-by-step like-term combination, and a polynomial operations reference table.
Adding and subtracting polynomials is one of the most fundamental skills in algebra, forming the basis for more advanced operations like polynomial multiplication, division, and factoring. The process involves combining like terms — terms that share the same variable raised to the same exponent — by adding or subtracting their coefficients. Although the concept is straightforward, handling polynomials with many terms or high degrees can become tedious and error-prone when done by hand.
Our Add & Subtract Polynomials Calculator streamlines this process by letting you enter up to four terms per polynomial (each defined by a coefficient and an exponent), choose whether to add or subtract, and instantly see the simplified result. The tool displays the combined polynomial, its degree, leading coefficient, constant term, the number of terms in the result, and a detailed step-by-step table showing how every pair of like terms was combined. Visual degree-comparison bars let you quickly see how the operation affects the polynomial's complexity. Eight ready-made presets cover common classroom problems so you can explore different scenarios without typing. Whether you're studying for an exam, verifying homework, or teaching algebra concepts, this calculator makes polynomial arithmetic quick, transparent, and mistake-free.
Add & Subtract Polynomials Calculator helps you solve add & subtract polynomials problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter your inputs once and immediately inspect Result Polynomial, Degree, Leading Coefficient to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
For like terms ax^n and bx^n: Addition → (a + b)x^n; Subtraction → (a − b)x^n. Unlike terms (different exponents) remain unchanged.
Result: Result Polynomial shown by the calculator
Using the preset "(3x²+2x+1) + (x²−x+4)", the calculator evaluates the add & subtract polynomials setup, applies the selected algebra rules, and reports Result Polynomial with supporting checks so you can verify each transformation.
This calculator takes the problem inputs and applies the relevant add & subtract polynomials relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Result Polynomial, Degree, Leading Coefficient, Constant Term to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
Like terms are terms that have the same variable raised to the same power. For example, 3x² and −5x² are like terms because both contain x². Only like terms can be added or subtracted directly.
Adding polynomials generally preserves the highest degree from either input. However, if the leading terms cancel out (e.g., 5x³ + (−5x³)), the resulting degree will be lower.
No. P₁ − P₂ is not the same as P₂ − P₁ because subtraction reverses the signs of the second polynomial. Addition of polynomials is commutative.
Type a minus sign before the number in the coefficient field, e.g., -3 for a term like −3x².
Empty fields are simply ignored. You can use as few as one term per polynomial; the calculator automatically skips any blank entries.
This tool is designed for integer exponents typical of polynomial algebra. Non-integer exponents produce results but technically create expressions that are not polynomials in the strict mathematical sense.