Question

Determine if the expression 2, x, to the power 42x
4
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer
Attempt 2 out of 5

The given expression ____
a polynomial.

Answer 1

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).

1. 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 \(4x^0\)).

2. 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**.