Math
Adding and Subtracting Polynomials Calculator
Type two polynomials such as 3x^2 - 2x + 5 and x^2 + 4x - 1 and the adding and subtracting polynomials calculator combines them term by term.
Subtraction first distributes the minus sign across the second polynomial, then each power of x is combined in its own column, so you can see exactly where each coefficient of the answer comes from.
Use ^ or ² for powers. Missing powers are fine; the calculator fills in 0 for them.
The polynomial to add to, or subtract from, P.
Try an example
Result
Result
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- Full statement
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- Like-term columns
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- Degree of the result
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- Leading coefficient
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- Constant term
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- Number of terms
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More details (2 more)
- Degrees of P and Q
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- Value at x = 1 (quick check)
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the adding and subtracting polynomials calculator solves
Polynomials are added by combining like terms: terms with the same variable raised to the same power. Only the The number multiplying a variable, like the 3 in 3x. change; the The small raised number saying how many times to multiply the base by itself. stay the same. Subtracting a polynomial means adding its opposite, so every sign in the second polynomial flips before the terms are combined.
Column method for (3x^2 - 2x + 5) - (x^2 + 4x - 1)
| Column | P | −Q | Sum |
|---|---|---|---|
| x^2 | 3 | -1 | 2 |
| x | -2 | -4 | -6 |
| constant | 5 | +1 | 6 |
Reading down the sum column gives 2x^2 - 6x + 6.
How to use it
- Choose Add or Subtract.
- Type P and Q with ^ for powers, for example 2x^3 - x + 4. Fractions such as (1/2)x are fine.
- Read the result in standard form, then open the steps to see each like-term column.
How to read the answer
The result is written in descending powers with every like term combined. Its degree is the highest power that survives, the leading coefficient is the number in front of that power, and the value at x = 1 is the sum of the coefficients, a quick way to check your own work.
Common mistakes and edge cases
- Subtracting only the first term of Q: the minus sign applies to every term, so -(x^2 + 4x - 1) = -x^2 - 4x + 1.
- Combining terms with different powers, such as adding x^2 and x.
- Changing the exponent when adding: 3x^2 + x^2 = 4x^2, not 4x^4.
- Forgetting a missing power: treat x^3 + 1 as x^3 + 0x^2 + 0x + 1 when lining up columns.
Worked examples
Add two quadratics
(3x^2 - 2x + 5) + (x^2 + 4x - 1) = 4x^2 + 2x + 4
Result
4x^2 + 2x + 4
Subtract and distribute the minus
(3x^2 - 2x + 5) - (x^2 + 4x - 1) = 2x^2 - 6x + 6
Result
2x^2 - 6x + 6
Degree drops when leading terms cancel
(x^2 + x) - (x^2 - 1) = x + 1
Result
x + 1
Missing powers and different degrees
(2x^3 + 1) + (x^2 - x) = 2x^3 + x^2 - x + 1
Result
2x^3 + x^2 - x + 1
Fraction coefficients
((1/2)x^2 + x) + ((1/3)x^2 - 2) = (5/6)x^2 + x - 2
Result
(5/6)x^2 + x - 2
Everything cancels
(x^2 - 4) - (x^2 - 4) = 0
Result
0
Two different variables
x and y in the same problem are rejected
Result
Error
Frequently asked questions
What are like terms?+
Terms with exactly the same variable part: 3x^2 and -5x^2 are like terms, but 3x^2 and 3x are not. Only like terms can be combined, and combining them adds the coefficients while keeping the exponent.
How do I subtract polynomials?+
Change the subtraction to adding the opposite: flip the sign of every term in the second polynomial, then add like terms. (3x^2 - 2x + 5) - (x^2 + 4x - 1) becomes 3x^2 - 2x + 5 - x^2 - 4x + 1 = 2x^2 - 6x + 6.
What is the degree of the sum of two polynomials?+
At most the larger of the two degrees. If the highest-power terms cancel, the degree is smaller. It can even be the zero polynomial, whose degree is undefined.
Do I need to write 0 for missing powers?+
Not for this calculator, but when working by hand it helps to line up columns: write x^3 + 1 as x^3 + 0x^2 + 0x + 1.
Can I add polynomials with fractions or decimals?+
Yes. Coefficients such as 1/2, 0.75, or 2/3 are converted to exact fractions, so (1/2)x + (1/3)x = (5/6)x with no rounding.
How can I check my answer?+
Plug x = 1 into both the original expression and your answer; both should give the same number. The calculator shows this value for the result.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
References
- OpenStax, Elementary Algebra 2e, Section 6.1 “Add and Subtract Polynomials” — Like terms, degree, and the column method.
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Last updated: September 4, 2026