Answer
Polynomial's degree: $3$
Leading term: $-5x^3$
Leading coefficient: $-5$
Work Step by Step
Let $p(x)=a_nx^n+a_{n-1}x^{n-1}+\dots+a_1x+a_0$ be a polynomial in standard form.
Let $f(x)=-5x^3+7x^2-x+2$.
$\textbf{The coefficient of a term $a_kx^k$}$ of a polynomial is the constant $a_k$.
For the polynomial $f$ we have:
- the coefficient of the term $-5x^3$ is $-5$;
- the coefficient of the term $7x^2$ is $7$;
- the coefficient of the term $-x$ is $-1$;
- the coefficient of the term $2$ is $2$.
$\textbf{The degree of a term $a_kx^k$}$ of a polynomial with one variable is the exponent of the variable, therefore $k$.
For the polynomial $f$ we have:
- the degree of the term $-5x^3$ is $3$;
- the degree of the term $7x^2$ is $2$;
- the degree of the term $-x$ is $1$;
- the degree of the term $2$ is $0$.
$\textbf{The degree of a polynomial}$ is the highest degree of its terms.
For the polynomial $f$ the degree is $3$.
$\textbf{The leading term}$ 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 $-5x^3$.
$\textbf{The leading coefficient}$ of a polynomial is the coefficient of the leading term.
For the polynomial $f$ the leading coefficient is $-5$.
