Find the Degree, Leading Term, and Leading Coefficient 5z+2z^3+3z^4

$5 z + 2 z^{3} + 3 z^{4}$

Step 1

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

Move $5 z$ .

$2 z^{3} + 3 z^{4} + 5 z$

Reorder $2 z^{3}$ and $3 z^{4}$ .

$3 z^{4} + 2 z^{3} + 5 z$

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.

$3 z^{4} \to 4$

$2 z^{3} \to 3$

$5 z \to 1$

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.

$3 z^{4}$

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.

$3 z^{4}$

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

$3$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $3 z^{4}$

Leading Coefficient: $3$