Find the Degree, Leading Term, and Leading Coefficient 5y^3-y^12+9+y^2

$5 y^{3} - y^{12} + 9 + y^{2}$

Step 1

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

Move $9$ .

$5 y^{3} - y^{12} + y^{2} + 9$

Reorder $5 y^{3}$ and $- y^{12}$ .

$- y^{12} + 5 y^{3} + y^{2} + 9$

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.

$- y^{12} \to 12$

$5 y^{3} \to 3$

$y^{2} \to 2$

$9 \to 0$

The largest exponent is the degree of the polynomial.

$12$

Step 3

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

$- y^{12}$

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.

$- y^{12}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $12$

Leading Term: $- y^{12}$

Leading Coefficient: $- 1$