Let's analyze the given function $g(x) = \frac{3 - x^2}{4}$.

Step 1: Determine if $g(x)$ is a polynomial

• A polynomial function consists of terms where the variable $x$ has only nonnegative integer exponents. Additionally, there should be no division by a variable.

Here:

• $g(x) = \frac{3 - x^2}{4}$ can be rewritten as: $g(x) = \frac{3}{4} - \frac{x^2}{4}$ Since the denominator 4 is a constant and not a variable, this expression is equivalent to a sum of terms with $x$-terms having nonnegative integer exponents.

Thus, $g(x)$ is a polynomial.

Step 2: Degree of the polynomial

The degree of a polynomial is determined by the highest power of $x$.

• Here, the term with the highest power of $x$ is $-\frac{x^2}{4}$, where the power is $2$.

So, the degree of the polynomial is 2.

Step 3: Leading term and constant term

• The leading term is the term with the highest degree, which is: $-\frac{x^2}{4}.$
• The constant term is the term without $x$, which is: $\frac{3}{4}.$

Final Answer:

• $g(x)$ is a polynomial.
• Degree: 2.
• Leading term: $-\frac{x^2}{4}$.
• Constant term: $\frac{3}{4}$.

Correct Choice:

• A. It is a polynomial of degree 2.

Do you need further clarification? Let me know if you'd like me to explain any step!

Related Questions:

1. What makes a function not a polynomial?
2. How can you identify the degree of a polynomial from its standard form?
3. What are the leading term and constant term in a polynomial?
4. How do you simplify a rational expression where the denominator is a constant?
5. Why does division by a variable disqualify a function from being a polynomial?

Tip:

The degree of a polynomial is always determined by the term with the largest exponent of $x$. Always simplify the function first!