1. What is Polynomial Addition/Subtraction?

Polynomial addition and subtraction involve combining like terms (terms with the same variable and exponent) from two or more polynomials. The result is a new polynomial that represents the sum or difference of the input polynomials.

2. How Does the Calculator Work?

The calculator performs polynomial operations by:

Process:

1. Parses each polynomial into individual terms
2. Combines like terms (terms with the same variable and exponent)
3. Applies the specified operation (addition or subtraction)
4. Returns the simplified result

3. Importance of Polynomial Operations

Applications: Polynomial operations are fundamental in algebra, calculus, physics, engineering, and computer graphics. They are used in curve fitting, solving equations, and modeling various phenomena.

4. Using the Calculator

Instructions:

• Enter polynomials in standard form (e.g., 3x^2 + 2x - 5)
• Use the caret (^) for exponents
• Include coefficients even if they are 1 (e.g., x^2 should be written as 1x^2)
• Select the operation (addition or subtraction)

5. Frequently Asked Questions (FAQ)

Q1: What is a polynomial?
A: A polynomial is an expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

Q2: How are like terms combined?
A: Like terms have the same variable(s) raised to the same power. Their coefficients are added or subtracted while keeping the variable part unchanged.

Q3: What is the degree of a polynomial?
A: The highest power of the variable in the polynomial. For example, 3x^2 + x - 5 has degree 2.

Q4: Can the calculator handle multiple variables?
A: This version handles single-variable polynomials. Terms with different variables are treated as unlike terms.

Q5: What about polynomial multiplication?
A: This calculator focuses on addition and subtraction. Multiplication requires the distributive property (FOIL method for binomials).