(-4x^4+3x^3-7x^2-x)+(-9x^3+7x^2-5x-1)

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 following polynomials:

(-4x⁴ + 3x³ - 7x² - x) + (-9x³ + 7x² - 5x - 1)

Understanding Polynomials

Before we start, let's briefly define what polynomials are:

• Polynomials are expressions consisting of variables and constants combined using addition, subtraction, multiplication, and non-negative integer exponents.

Adding Polynomials

To add polynomials, we follow these simple steps:

1. Identify like terms: Look for terms that have the same variable and exponent. For example, 3x³ and -9x³ are like terms, while -7x² and -5x are not.

2. Combine like terms: Add the coefficients of the like terms.

3. Simplify the expression: Write the resulting polynomial in descending order of exponents.

Applying the Steps to Our Example

Let's apply these steps to our given polynomials:

Step 1: Identify like terms:

• -4x⁴ (no like term)
• 3x³ and -9x³
• -7x² and 7x²
• -x and -5x
• -1 (no like term)

Step 2: Combine like terms:

• -4x⁴
• 3x³ + (-9x³) = -6x³
• -7x² + 7x² = 0
• -x + (-5x) = -6x
• -1

Step 3: Simplify the expression:

-4x⁴ - 6x³ - 6x - 1

Therefore, the sum of the given polynomials is -4x⁴ - 6x³ - 6x - 1.