(8x^3-2x^2+6x-18)+(4x^3-x^2-5x+7)

Jasonbradley

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Jun 16, 2024

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Adding Polynomials: (8x^3-2x^2+6x-18)+(4x^3-x^2-5x+7)

This article will guide you through the process of adding two polynomials: (8x^3-2x^2+6x-18) and (4x^3-x^2-5x+7).

Understanding Polynomials

Polynomials are expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. They involve non-negative integer exponents.

Adding Polynomials

To add polynomials, we simply combine like terms. Like terms are those with the same variable and exponent.

Step-by-Step Solution

1. Write the polynomials side-by-side:

   (8x^3 - 2x^2 + 6x - 18) + (4x^3 - x^2 - 5x + 7)

2. Identify like terms:

   • x^3 terms: 8x^3 + 4x^3
   • x^2 terms: -2x^2 - x^2
   • x terms: 6x - 5x
   • Constant terms: -18 + 7

3. Combine like terms:

   (8x^3 + 4x^3) + (-2x^2 - x^2) + (6x - 5x) + (-18 + 7)

4. Simplify:

   12x^3 - 3x^2 + x - 11

Result

The sum of the polynomials (8x^3-2x^2+6x-18) and (4x^3-x^2-5x+7) is 12x^3 - 3x^2 + x - 11.