(3x^2+2x+1)+(2x^2-4x-5)+(3x-1)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomials: A Step-by-Step Guide

This article will walk you through the process of simplifying the polynomial expression: (3x^2 + 2x + 1) + (2x^2 - 4x - 5) + (3x - 1)

Understanding the Basics

Before we dive into the simplification, let's quickly recap some key concepts:

• Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
• Terms: The individual parts of a polynomial separated by addition or subtraction.
• Like Terms: Terms that have the same variables raised to the same powers. For example, 3x^2 and 2x^2 are like terms, while 3x^2 and 2x are not.

Simplifying the Expression

1. Identify Like Terms: Look for terms that have the same variable and exponent.

   • x^2 terms: 3x^2 and 2x^2
   • x terms: 2x, -4x, and 3x
   • Constant terms: 1, -5, and -1

2. Combine Like Terms: Add or subtract the coefficients of like terms.

   • x^2 terms: 3x^2 + 2x^2 = 5x^2
   • x terms: 2x - 4x + 3x = x
   • Constant terms: 1 - 5 - 1 = -5

3. Write the Simplified Expression: Combine the results of step 2.

**(3x^2 + 2x + 1) + (2x^2 - 4x - 5) + (3x - 1) = ** 5x^2 + x - 5

Conclusion

By following these simple steps, we have successfully simplified the given polynomial expression. Remember that combining like terms is essential for writing polynomials in their simplest form.