To determine the leading coefficient and degree of the polynomial
[tex]\[
-9v^2 + 12v - v^4 + 1,
\][/tex]
follow these steps:
1. Standard Form of the Polynomial: Write the polynomial in standard form, which arranges the terms by descending power of the variable [tex]\( v \)[/tex]. The polynomial in standard form is:
[tex]\[
-v^4 -9v^2 + 12v + 1.
\][/tex]
2. Identify the Degree: The degree of a polynomial is the highest power of the variable [tex]\( v \)[/tex] in the polynomial. In this polynomial, the term with the highest power of [tex]\( v \)[/tex] is [tex]\(-v^4\)[/tex]. Therefore, the degree of this polynomial is:
[tex]\[
4.
\][/tex]
3. Identify the Leading Coefficient: The leading coefficient is the coefficient of the term with the highest power of [tex]\( v \)[/tex]. In this case, the term with the highest power is [tex]\(-v^4\)[/tex], and its coefficient is:
[tex]\[
-1.
\][/tex]
To summarize:
- The degree of the polynomial [tex]\(-9v^2 + 12v - v^4 + 1\)[/tex] is [tex]\( 4 \)[/tex].
- The leading coefficient of the polynomial [tex]\(-9v^2 + 12v - v^4 + 1\)[/tex] is [tex]\( -1 \)[/tex].
