(2x^4-3x+8)+(3x^3+5x^2-2x+7)

Jasonbradley

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Jun 16, 2024

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Adding Polynomials: A Step-by-Step Guide

This article will guide you through the process of adding the two polynomials: (2x^4 - 3x + 8) and (3x^3 + 5x^2 - 2x + 7).

Understanding Polynomials

Before we begin, let's define what a polynomial is. A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.

Key terms:

• Variable: A symbol representing an unknown value (e.g., x, y, z).
• Coefficient: A number multiplied by a variable (e.g., 2 in 2x).
• Term: A single variable or a product of a variable and a coefficient (e.g., 2x^4, -3x, 8).

Adding the Polynomials

1. Rearrange the terms:

   • Write the polynomials in descending order of their exponents (highest to lowest):
     • 2x^4 - 3x + 8
     • 3x^3 + 5x^2 - 2x + 7

2. Combine like terms:

   • Identify terms with the same variable and exponent.

   • Add the coefficients of these terms:

     • 2x^4 + 3x^3 + 5x^2 + (-3x - 2x) + (8 + 7)

3. Simplify:

   • Combine the coefficients of like terms:

     • 2x^4 + 3x^3 + 5x^2 - 5x + 15

Final Result

The sum of the two polynomials (2x^4 - 3x + 8) and (3x^3 + 5x^2 - 2x + 7) is 2x^4 + 3x^3 + 5x^2 - 5x + 15.