Adding Polynomials Calculator
Add polynomials with step-by-step solutions and color-coded like terms
Enter using format: 3x^2 + 5x - 7
Enter using format: 2x^2 - 3x + 4
How to Add Polynomials
Adding polynomials is a fundamental algebraic operation that involves combining like terms. This calculator makes the process easy by showing you each step and helping you understand the underlying mathematical concepts.
What Are Like Terms?
Like terms are terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms because they both contain x². However, 3x² and 5x are not like terms because the exponents are different.
Steps to Add Polynomials
- Write in Standard Form: Arrange terms in descending order of exponents
- Align Like Terms: Group terms with the same exponent together
- Add Coefficients: Add the coefficients of like terms
- Simplify: Write the result in standard form
Example: Adding Polynomials
Let's add (3x² + 5x - 7) + (2x² - 3x + 4):
- x² terms: 3x² + 2x² = 5x²
- x terms: 5x + (-3x) = 2x
- Constant terms: -7 + 4 = -3
- Result: 5x² + 2x - 3
Common Mistakes to Avoid
- Don't add terms with different exponents (3x² and 5x cannot be combined)
- Pay attention to negative signs when adding coefficients
- Always arrange the final answer in standard form (descending exponents)
- Don't forget to include all terms, even if some cancel to zero
Frequently Asked Questions
What does it mean to add polynomials?
Adding polynomials means combining two or more polynomials by adding their like terms. Like terms are terms with the same variable and exponent. You add only the coefficients of like terms while keeping the variable and exponent the same.
How do I combine like terms?
To combine like terms, add their coefficients while keeping the variable and exponent unchanged. For example, 3x² + 5x² = 8x². The variable part (x²) stays the same, and only the coefficients (3 and 5) are added.
Can I add terms with different exponents?
No, you cannot combine terms with different exponents. For example, 3x² and 5x are not like terms and must remain separate in the answer. Only terms with identical variable parts can be combined.
What if one polynomial has a term the other doesn't?
If one polynomial has a term that the other doesn't, you can think of the missing term as having a coefficient of 0. For example, if one polynomial has 5x² and the other doesn't have an x² term, you can think of it as 5x² + 0x² = 5x².
How do I handle negative coefficients when adding?
When adding polynomials with negative coefficients, treat the negative sign as part of the coefficient. For example, 3x + (-5x) = -2x. Be careful with signs, especially when dealing with subtraction or multiple negative terms.
What is standard form for a polynomial?
Standard form for a polynomial means writing terms in descending order of exponents, from highest to lowest. For example, 5x³ + 2x² - 3x + 7 is in standard form. This makes polynomials easier to read and compare.
Can this calculator add more than two polynomials?
Currently, this calculator adds two polynomials at a time. To add three or more polynomials, add the first two, then add the result to the third polynomial, and so on. The process is the same regardless of how many polynomials you're adding.
Is adding polynomials the same as polynomial addition?
Yes, "adding polynomials" and "polynomial addition" are two ways of describing the same operation. Both refer to the process of combining two or more polynomials by adding their corresponding like terms.
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