Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the following polynomial expression:
(−5x⁴ + 6x³ − 43) + (6x⁵ − x² + 12x + 12)
Understanding the Basics
Before we begin, let's recall some key concepts:
 Polynomials: Expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
 Terms: Individual parts of a polynomial separated by addition or subtraction.
 Like Terms: Terms with the same variable and exponent.
Simplifying the Expression

Remove the parentheses: Since we are adding the two polynomials, the parentheses are unnecessary.
( −5x⁴ + 6x³ − 43) + (6x⁵ − x² + 12x + 12) = −5x⁴ + 6x³ − 43 + 6x⁵ − x² + 12x + 12

Rearrange terms: Group like terms together.
6x⁵ − 5x⁴ + 6x³ − x² + 12x − 43 + 12

Combine like terms: Add or subtract the coefficients of the like terms.
6x⁵ − 5x⁴ + 6x³ − x² + 12x − 31
Final Result
The simplified form of the polynomial expression is:
6x⁵ − 5x⁴ + 6x³ − x² + 12x − 31
Key Takeaways
 Combining Like Terms: The key to simplifying polynomial expressions is to identify and combine like terms.
 Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying.
 Understanding Polynomial Basics: A strong understanding of polynomial terminology and structure is essential for successful simplification.