(8x^2+6x+10)+(5x^2-4x+9)

Jasonbradley

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Jun 16, 2024

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Adding Polynomials: (8x^2+6x+10)+(5x^2-4x+9)

This article will guide you through the process of adding the polynomials (8x^2+6x+10) and (5x^2-4x+9).

Understanding Polynomials

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

Adding Polynomials

To add polynomials, we simply combine like terms. Like terms have the same variables raised to the same powers. Here's how we add our two polynomials:

1. Identify like terms:

   • x² terms: 8x² and 5x²
   • x terms: 6x and -4x
   • Constant terms: 10 and 9

2. Combine like terms:

   • (8x² + 5x²) + (6x - 4x) + (10 + 9)

3. Simplify:

   • 13x² + 2x + 19

The Result

Therefore, the sum of the polynomials (8x² + 6x + 10) and (5x² - 4x + 9) is 13x² + 2x + 19.