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(−5x4+6x3−43)+(6x5−x2+12x+12)

2 min read Jun 17, 2024
(−5x4+6x3−43)+(6x5−x2+12x+12)

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

  1. 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

  2. Rearrange terms: Group like terms together.

    6x⁵ − 5x⁴ + 6x³ − x² + 12x − 43 + 12

  3. 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.

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