Certainly! Let's analyze and understand the given mathematical expression step by step: [tex]\( x^4 + 4 \)[/tex].
### Step 1: Understanding the Expression
We see that this is a polynomial expression in terms of [tex]\( x \)[/tex]. Specifically, it is a fourth-degree polynomial, given by [tex]\( x^4 \)[/tex], with a constant term of 4 added to it.
### Step 2: Identifying Components
The polynomial expression can be broken down into its components:
- [tex]\( x^4 \)[/tex]: This term represents [tex]\( x \)[/tex] raised to the power of 4.
- [tex]\( + 4 \)[/tex]: This is a constant term added to the polynomial.
### Step 3: Recognition of Polynomial Type
The polynomial is already simplified. We recognize that the expression [tex]\( x^4 + 4 \)[/tex] doesn't factor easily over the real numbers because it lacks the presence of real number roots that can simplify it further without utilizing complex numbers.
### Step 4: Expressing the Final Answer
Thus, the expression [tex]\( x^4 + 4 \)[/tex] remains as is, and any further simplification or factorization, if required, would necessitate extending our number system to include complex numbers, which is outside this current analysis.
### Conclusion
The given expression [tex]\( x^4 + 4 \)[/tex] is a straightforward polynomial which is already in its simplest form for the context given.
Final Answer:
[tex]\[ x^4 + 4 \][/tex]
This represents the final form of the polynomial expression.
