Find the Degree, Leading Term, and Leading Coefficient 3xy^3+5x^5y^3+x^3y^7-7x^2y

$3 x y^{3} + 5 x^{5} y^{3} + x^{3} y^{7} - 7 x^{2} y$

Step 1

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

Move $3 x y^{3}$ .

$5 x^{5} y^{3} + x^{3} y^{7} + 3 x y^{3} - 7 x^{2} y$

Reorder $5 x^{5} y^{3}$ and $x^{3} y^{7}$ .

$x^{3} y^{7} + 5 x^{5} y^{3} + 3 x y^{3} - 7 x^{2} y$

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.

$x^{3} y^{7} \to 10$

$5 x^{5} y^{3} \to 8$

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

$- 7 x^{2} y \to 3$

The largest exponent is the degree of the polynomial.

$10$

Step 3

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

$x^{3} y^{7}$

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.

$x^{3} y^{7}$

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

$1$

Step 5

List the results.

Polynomial Degree: $10$

Leading Term: $x^{3} y^{7}$

Leading Coefficient: $1$