Find the Degree, Leading Term, and Leading Coefficient 8z+9-3z^2-4z^4-z^3

$8 z + 9 - 3 z^{2} - 4 z^{4} - z^{3}$

Step 1

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

Move $9$ .

$8 z - 3 z^{2} - 4 z^{4} - z^{3} + 9$

Move $8 z$ .

$- 3 z^{2} - 4 z^{4} - z^{3} + 8 z + 9$

Move $- 3 z^{2}$ .

$- 4 z^{4} - z^{3} - 3 z^{2} + 8 z + 9$

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.

$- 4 z^{4} \to 4$

$- z^{3} \to 3$

$- 3 z^{2} \to 2$

$8 z \to 1$

$9 \to 0$

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.

$- 4 z^{4}$

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.

$- 4 z^{4}$

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

$- 4$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- 4 z^{4}$

Leading Coefficient: $- 4$