The expression you provided seems to be a bit unclear as it includes both numbers and variables, and it may contain formatting issues. However, I'll interpret it as:
\[ 2x^{42} + 4 \]
To determine if this expression is a polynomial, we consider the definition of a polynomial. A polynomial in one variable \(x\) is an expression that can be written in the form:
\[ a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 \]
where \(n\) is a non-negative integer, and \(a_n, a_{n-1}, \ldots, a_0\) are constants (coefficients).
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The expression \(2x^{42} + 4\) consists of two terms: \(2x^{42}\) (which is a polynomial term because it has a non-negative integer exponent) and \(4\) (a constant term, which can be considered as \(4x^0\)).
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Since there are no negative or fractional powers of \(x\), and there are no variables in the denominators, \(2x^{42} + 4\) satisfies the requirements for being a polynomial.
Now, we identify the type and degree of the polynomial:
- Type: The expression is a polynomial of degree 42 (since the highest power of \(x\) is 42).
- Degree: The degree of the polynomial is 42.
Therefore, the final answer is:
The given expression is a polynomial. It is a polynomial of degree 42.