Find the Degree, Leading Term, and Leading Coefficient 2xy^4+2x^2y-3y^2+10x^3

$2 x y^{4} + 2 x^{2} y - 3 y^{2} + 10 x^{3}$

Step 1

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

Move $- 3 y^{2}$ .

$2 x y^{4} + 2 x^{2} y + 10 x^{3} - 3 y^{2}$

Move $2 x^{2} y$ .

$2 x y^{4} + 10 x^{3} + 2 x^{2} y - 3 y^{2}$

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.

$2 x y^{4} \to 5$

$10 x^{3} \to 3$

$2 x^{2} y \to 3$

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

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$2 x y^{4}$

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.

$2 x y^{4}$

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

$2$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $2 x y^{4}$

Leading Coefficient: $2$