Polynomial calculator
Add, subtract, or multiply two polynomials in x.
What this calculator covers
Use this polynomial calculator to add, subtract, or multiply two polynomials written in terms of x.
The result is normalized in descending powers so the like-term work is easy to audit before you move on to factoring or solving.
Frequently asked questions
- How do I enter a polynomial expression?
- Type terms using `^` for exponents, `*` or implied multiplication for coefficients, and `+` or `-` between terms. For example, `x^2+2x+1` or `3x^3-x+5`. The variable must be `x`, and only non-negative integer exponents are supported.
- What does it mean to normalize a polynomial?
- Normalizing rewrites the polynomial so terms are listed in order from the highest exponent down to the lowest. This makes it easy to line up matching powers of x when adding or subtracting two expressions.
- How does polynomial multiplication work here?
- Each term in the first polynomial is multiplied by every term in the second polynomial, then all the resulting products that share the same power of x are combined. This is the distributive property applied systematically across all term pairs.
- Can I use this for polynomials with more than one variable?
- No. The calculator is limited to single-variable polynomials in x. Expressions containing other variables or multiple variables together are not supported and will produce an error.
Tool
Run the calculation
Result
RESULT · POLYNOMIAL
â„–210
Primary result
x^2 + 3x - 2
Adding x^2 + 2x + 1 and x - 3 gives x^2 + 3x - 2.
- First polynomial
- x^2 + 2x + 1
- Second polynomial
- x - 3
- Result
- x^2 + 3x - 2
- Degree
- 2
Step-by-step solution
- 1.Rewrite each expression in descending powers of x: x^2 + 2x + 1 and x - 3.
- 2.Align the matching exponents and add the like-term coefficients.
- 3.Read the final polynomial as x^2 + 3x - 2.
Walkthrough
Visual walkthrough
Polynomial arithmetic is bookkeeping by exponent: keep powers of x aligned, then combine or distribute them carefully.
01
Normalize both inputs
x^2 + 2x + 1 and x - 3
Writing each polynomial in descending powers makes the exponent structure easy to compare.
02
Work coefficient by coefficient
Align the matching exponents and add the like-term coefficients.
03
Collect the final polynomial
Once the like powers are combined, the remaining coefficients define the result polynomial.
x^2 + 3x - 2