## Simplifying the Expression: 0.5(x^4-3) + 12

This article will guide you through the process of simplifying the algebraic expression **0.5(x^4-3) + 12**. Let's break it down step by step:

### 1. Distribute the 0.5

The first step is to distribute the 0.5 to both terms inside the parentheses:

**0.5 * x^4 = 0.5x^4****0.5 * -3 = -1.5**

Now the expression looks like this: **0.5x^4 - 1.5 + 12**

### 2. Combine Constant Terms

Next, we combine the constant terms -1.5 and 12:

**-1.5 + 12 = 10.5**

The simplified expression is now: **0.5x^4 + 10.5**

### Final Simplified Expression

Therefore, the simplified form of the expression **0.5(x^4-3) + 12** is **0.5x^4 + 10.5**.

This expression represents a **quartic polynomial**, which is a polynomial with a highest power of 4.