## Simplifying and Combining Polynomials

This article will explore how to simplify and combine the following polynomials:

**5x - 2x^(2) - 8****8x^(2) - 7x - 9****3 + 7x^(2) - 2x**

### Understanding Polynomials

Polynomials are mathematical expressions consisting of variables and constants combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a constant and one or more variables raised to non-negative integer powers.

### Simplifying Polynomials

Simplifying polynomials involves combining like terms. Like terms are terms with the same variable(s) raised to the same power.

Here's how we simplify each polynomial:

**1. 5x - 2x^(2) - 8**

This polynomial is already in its simplest form. We can rearrange the terms for easier reading:

**-2x^(2) + 5x - 8**

**2. 8x^(2) - 7x - 9**

This polynomial is also in its simplest form.

**3. 3 + 7x^(2) - 2x**

Rearranging terms for clarity:

**7x^(2) - 2x + 3**

### Combining Polynomials

To combine polynomials, we simply add or subtract their like terms.

Let's combine the three simplified polynomials:

**(-2x^(2) + 5x - 8) + (8x^(2) - 7x - 9) + (7x^(2) - 2x + 3)**

**Combine the x^(2) terms:**-2x^(2) + 8x^(2) + 7x^(2) = 13x^(2)**Combine the x terms:**5x - 7x - 2x = -4x**Combine the constant terms:**-8 - 9 + 3 = -14

The combined polynomial is:

**13x^(2) - 4x - 14**

### Conclusion

By understanding the concepts of like terms and simplification, we can easily combine polynomials to create a single, simplified expression. This process is fundamental in various mathematical operations and applications.