(8x^4-3/5x^2-1)+(3x^3+1/5x^2+7x+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 two polynomials: (8x^4 - 3/5x^2 - 1) + (3x^3 + 1/5x^2 + 7x + 1)

Understanding Polynomials

Polynomials are expressions containing variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial consists of a coefficient and a variable raised to a non-negative integer power.

Combining Like Terms

To add polynomials, we combine like terms. Like terms have the same variable and the same exponent. For instance, 3x^2 and -5x^2 are like terms, while 3x^2 and 3x^3 are not.

Step-by-Step Solution

1. Rewrite the expression: (8x^4 - 3/5x^2 - 1) + (3x^3 + 1/5x^2 + 7x + 1)

2. Remove the parentheses: 8x^4 - 3/5x^2 - 1 + 3x^3 + 1/5x^2 + 7x + 1

3. Identify like terms:

   • x^4 terms: 8x^4
   • x^3 terms: 3x^3
   • x^2 terms: -3/5x^2 + 1/5x^2
   • x terms: 7x
   • Constant terms: -1 + 1

4. Combine like terms:

   • 8x^4 + 3x^3 + (-3/5 + 1/5)x^2 + 7x + (-1 + 1)

5. Simplify:

   • 8x^4 + 3x^3 - 2/5x^2 + 7x

The Result

The sum of the given polynomials is 8x^4 + 3x^3 - 2/5x^2 + 7x.

This expression is a polynomial in standard form, arranged in descending order of exponents.