Add The Following Polynomials (x^3-2x^2+3)+(2x^3+3x^2-1)

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Sep 02, 2024

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Adding Polynomials: (x³ - 2x² + 3) + (2x³ + 3x² - 1)

This problem involves adding two polynomials. Here's how to solve it:

Understanding Polynomials

Polynomials are expressions made up of variables and constants, 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 variable and the same exponent.

Steps:

1. Identify Like Terms: In our problem, we have:

   • x³ terms: x³ and 2x³
   • x² terms: -2x² and 3x²
   • Constant terms: 3 and -1

2. Combine Like Terms:

   • (x³ + 2x³) = 3x³
   • (-2x² + 3x²) = x²
   • (3 - 1) = 2

3. Write the Result: The sum of the polynomials is: 3x³ + x² + 2

Summary

Therefore, the sum of the polynomials (x³ - 2x² + 3) + (2x³ + 3x² - 1) is 3x³ + x² + 2.