Adding Polynomials: A StepbyStep Guide
This article will guide you through the process of adding the two polynomials: (8x⁴ + 2x²  1) + (3x³  5x² + 7x + 1).
Understanding Polynomials
Before we begin, let's define what polynomials are:
 Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents of the variables are nonnegative integers.
Adding Polynomials: The Process

Identify Like Terms: Like terms are terms that have the same variable and exponent. In our example, the like terms are:
 x⁴ terms: 8x⁴
 x³ terms: 3x³
 x² terms: 2x² and 5x²
 x terms: 7x
 Constant terms: 1 and 1

Combine Like Terms: Add the coefficients of the like terms together.
 x⁴ terms: 8x⁴
 x³ terms: 3x³
 x² terms: 2x²  5x² = 3x²
 x terms: 7x
 Constant terms: 1 + 1 = 0

Write the Result: Arrange the terms in descending order of their exponents.
Therefore, the sum of the two polynomials is 8x⁴ + 3x³  3x² + 7x.
Conclusion
Adding polynomials is a straightforward process. By identifying and combining like terms, you can simplify the expression and obtain the sum of the polynomials. Remember to arrange the terms in descending order of their exponents for a clear and organized result.