Find the Degree, Leading Term, and Leading Coefficient -3y^11-y^8+7+2y^12

$- 3 y^{11} - y^{8} + 7 + 2 y^{12}$

Step 1

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

Move $7$ .

$- 3 y^{11} - y^{8} + 2 y^{12} + 7$

Move $- y^{8}$ .

$- 3 y^{11} + 2 y^{12} - y^{8} + 7$

Reorder $- 3 y^{11}$ and $2 y^{12}$ .

$2 y^{12} - 3 y^{11} - y^{8} + 7$

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.

$2 y^{12} \to 12$

$- 3 y^{11} \to 11$

$- y^{8} \to 8$

$7 \to 0$

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.

$2 y^{12}$

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.

$2 y^{12}$

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

$2$

Step 5

List the results.

Polynomial Degree: $12$

Leading Term: $2 y^{12}$

Leading Coefficient: $2$