Adding Polynomials: A StepbyStep Guide
This article will guide you through the process of adding two polynomials: (9x⁴  3x³ + 4x² + 5x + 7) + (11x⁴  4x²  11x  9)
Understanding Polynomials
Polynomials are algebraic expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a coefficient and one or more variables raised to nonnegative integer powers.
Adding Polynomials
To add polynomials, we combine like terms. Like terms are terms that have the same variables raised to the same powers.
Here's how to add the given polynomials:

Arrange the terms in descending order of their exponents: (9x⁴  3x³ + 4x² + 5x + 7) + (11x⁴  4x²  11x  9)

Identify like terms:
 x⁴ terms: 9x⁴ + 11x⁴
 x³ terms: 3x³
 x² terms: 4x²  4x²
 x terms: 5x  11x
 Constant terms: 7  9

Combine like terms by adding their coefficients:
 (9 + 11)x⁴  3x³ + (4  4)x² + (5  11)x + (7  9)

Simplify the expression:
 20x⁴  3x³  6x  2
Final Result
Therefore, the sum of the given polynomials is 20x⁴  3x³  6x  2.
Key Points
 Remember to add only like terms.
 Always combine the coefficients of the like terms.
 Organize the terms in descending order of their exponents.
 Simplify the expression by combining constants.