Let's address the given polynomial step by step:
The polynomial provided is:
[tex]\[
-x^2 - 4
\][/tex]
1. Determine the type of polynomial:
- A polynomial is classified based on the highest power of the variable [tex]\( x \)[/tex]. Here, the highest power of [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex].
- A polynomial with the highest power of [tex]\( 2 \)[/tex] is called a quadratic polynomial.
2. Identify the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest power.
- In this polynomial, the term with the highest power is [tex]\( -x^2 \)[/tex].
- The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( -1 \)[/tex]. Therefore, the leading coefficient is [tex]\( -1 \)[/tex].
3. Identify the constant term:
- The constant term is the term without the variable [tex]\( x \)[/tex].
- In this polynomial, the constant term is [tex]\( -4 \)[/tex].
4. Identify the leading term:
- The leading term is the term with the highest power of [tex]\( x \)[/tex].
- Here, the leading term is [tex]\( -x^2 \)[/tex].
Now, let's fill in the blanks based on our analysis:
The expression represents a quadratic polynomial with [tex]\(-x^2 - 4\)[/tex] and the leading coefficient is -1. The constant term is -4, the leading term is -x^2.
