Find the Degree, Leading Term, and Leading Coefficient m+m^3-8m^4

$m + m^{3} - 8 m^{4}$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Move $m$ .

$m^{3} - 8 m^{4} + m$

Reorder $m^{3}$ and $- 8 m^{4}$ .

$- 8 m^{4} + m^{3} + m$

Step 2

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- 8 m^{4} \to 4$

$m^{3} \to 3$

$m \to 1$

The largest exponent is the degree of the polynomial.

$4$

Step 3

The leading term in a polynomial is the term with the highest degree.

$- 8 m^{4}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$- 8 m^{4}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 8$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- 8 m^{4}$

Leading Coefficient: $- 8$