Polynomial Addition Calculator

How it is calculated

Each polynomial is a list of coefficients written from the highest power down to the constant term, separated by spaces, commas or semicolons. So 3 -2 0 5 means 3x³ − 2x² + 0x + 5. Both lists are aligned at the constant term, the shorter one is padded with zeros on the high-degree side, and the coefficients are added position by position: ck = ak + bk. Leading zeros in the sum are dropped, so if the top terms cancel the degree falls, and a total cancellation gives a single 0 with degree 0. Missing powers must be entered as 0. Decimals use a dot on this page. Anything that is not a number, an empty list, or a coefficient too large to show exactly (above about 9 × 10¹⁵) gives no result. Coefficients are shown to at most four decimals with trailing zeros removed.

Common mistakes

• Leaving out a coefficient for a missing power. Writing 3 -2 5 for 3x³ − 2x² + 5 gives a quadratic, so type the 0 for the x term.
• Entering the coefficients from the lowest power up. The tool expects the highest power first, so reversed lists give the wrong polynomial.
• Using a decimal comma such as 1,5 on the English page. A comma separates coefficients here, so 1,5 is read as the two numbers 1 and 5 and the degree comes out one higher than intended; write 1.5.
• Expecting the degree of the sum to be the larger of the two degrees. When the leading terms cancel, the degree is lower, and 2 3 plus −2 −3 gives just 0.
• Typing the variable or exponents, for example 3x^3. The fields take only numbers, and text shows no result.