Alright, let's analyze the given polynomial step by step:
The polynomial provided is
[tex]\[ -4x^5 - x^4 - 7 - \frac{1}{4}x \][/tex]
1. Type of Polynomial:
The expression given is a polynomial.
2. Number of Terms:
To determine the number of terms, we count each distinct portion separated by addition or subtraction:
[tex]\[ -4x^5, -x^4, -7, -\frac{1}{4}x \][/tex]
Therefore, it has 4 terms.
3. Constant Term:
The constant term in a polynomial is the term that does not contain any variable. Here, the constant term is:
[tex]\[ -7 \][/tex]
4. Leading Term:
The leading term is the term with the highest exponent. In this polynomial, the term with the highest exponent is:
[tex]\[ -4x^5 \][/tex]
5. Leading Coefficient:
The coefficient of the leading term is called the leading coefficient. Here, the coefficient of [tex]\( -4x^5 \)[/tex] is:
[tex]\[ -4 \][/tex]
Putting it all together, the answers to the questions are:
- The expression represents a polynomial with 4 terms.
- The constant term is [tex]\( -7 \)[/tex].
- The leading term is [tex]\( -4x^5 \)[/tex].
- The leading coefficient is [tex]\( -4 \)[/tex].
Therefore, the completed sentence is:
The expression represents a polynomial with 4 terms. The constant term is [tex]\(-7\)[/tex], the leading term is [tex]\(-4x^5\)[/tex], and the leading coefficient is [tex]\(-4\)[/tex].
