Answer
Polynomial's degree: $7$
Leading term: $-7xy^6$
Leading coefficient: $-7$
Work Step by Step
Let $f(x,y)=8x^4y^2-7xy^6-x^3y$.
$\textbf{The coefficient of a term $a_kx^py^q$}$ of a polynomial is the constant $a_k$.
For the polynomial $f$ we have:
- the coefficient of the term $8x^4y^2$ is $8$;
- the coefficient of the term $-7xy^6$ is $-7$;
- the coefficient of the term $-x^3y$ is $-1$.
$\textbf{The degree of a term $a_kx^py^q$}$ of a polynomial with two variables is the sum of the exponents of the variables.
For the polynomial $f$ we have:
- the degree of the term $8x^4y^2$ is $4+2=6$;
- the degree of the term $-7xy^6$ is $1+6=7$;
- the degree of the term $-x^3y$ is $3+1=4$.
$\textbf{The degree of a polynomial}$ is the highest degree of its terms.
For the polynomial $f$, the degree is $7$.
$\textbf{The leading term}$ of a polynomial is the term containing the highest power of the variable (the term with the highest degree).
For the polynomial $f$ the leading term is $-7xy^6$.
$\textbf{The leading coefficient}$ of a polynomial is the coefficient of the leading term.
For the polynomial $f$ the leading coefficient is $-7$.
