## Simplifying Polynomial Expressions: (x^2 + x + 5) + (3x^2 - 10x + 4)

This article will guide you through the process of simplifying the given polynomial expression: **(x^2 + x + 5) + (3x^2 - 10x + 4)**

### Understanding the Problem

The expression involves two polynomials:

**(x^2 + x + 5)****(3x^2 - 10x + 4)**

We are asked to **add** these two polynomials.

### Simplifying the Expression

**1. Remove the Parentheses:**

Since we are adding the two polynomials, the parentheses are unnecessary. We can simply rewrite the expression as:

x^2 + x + 5 + 3x^2 - 10x + 4

**2. Combine Like Terms:**

**x^2 terms:**x^2 + 3x^2 = 4x^2**x terms:**x - 10x = -9x**Constant terms:**5 + 4 = 9

**3. Write the Simplified Expression:**

Combining the like terms, we get the simplified expression:

**4x^2 - 9x + 9**

### Conclusion

Therefore, the simplified form of the expression (x^2 + x + 5) + (3x^2 - 10x + 4) is **4x^2 - 9x + 9**. This process demonstrates the fundamental principles of combining polynomials by identifying and combining like terms.