Questions: Determine whether the expression is a polynomial. If it is, state how many terms and vari 4 x^2-2 x+4 The expression is Select the correct choice below and fill in any answer boxes in your choice. A. The polynomial has term(s) and variable(s). B. The expression is not a polynomial. Select the correct choice below and fill in any answer boxes in your choice. A. Its degree is . B. The expression is not a polynomial.

Solution Steps

To determine whether the given expression is a polynomial, we need to check if it consists of terms that are non-negative integer powers of the variable \( x \). If it is a polynomial, we will count the number of terms and variables, and determine its degree.

The expression \( 4x^2 - 2x + 4 \) consists of terms that are non-negative integer powers of the variable \( x \). Each term can be expressed as follows:

• \( 4x^2 \) (degree 2)
• \( -2x \) (degree 1)
• \( 4 \) (degree 0)

Since all terms meet the criteria for polynomials, we conclude that the expression is indeed a polynomial.

The expression has three distinct terms: \( 4x^2 \), \( -2x \), and \( 4 \). There is only one variable present, which is \( x \).

The degree of a polynomial is defined as the highest power of the variable in the expression. In this case, the highest power of \( x \) is 2 (from the term \( 4x^2 \)). Therefore, the degree of the polynomial is 2.

Final Answer