Find the Degree, Leading Term, and Leading Coefficient 27+3xy^3-12x^2y^2-10y

$27 + 3 x y^{3} - 12 x^{2} y^{2} - 10 y$

Step 1

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

Move $27$ .

$3 x y^{3} - 12 x^{2} y^{2} - 10 y + 27$

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

$- 12 x^{2} y^{2} + 3 x y^{3} - 10 y + 27$

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.

$- 12 x^{2} y^{2} \to 4$

$3 x y^{3} \to 4$

$- 10 y \to 1$

$27 \to 0$

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.

$- 12 x^{2} y^{2}$

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.

$- 12 x^{2} y^{2}$

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

$- 12$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- 12 x^{2} y^{2}$

Leading Coefficient: $- 12$