Find the Degree, Leading Term, and Leading Coefficient 6x^4y^5z^2-5x^2y^3z^10+3xy^5

$6 x^{4} y^{5} z^{2} - 5 x^{2} y^{3} z^{10} + 3 x y^{5}$

Step 1

Reorder $6 x^{4} y^{5} z^{2}$ and $- 5 x^{2} y^{3} z^{10}$ .

$- 5 x^{2} y^{3} z^{10} + 6 x^{4} y^{5} z^{2} + 3 x y^{5}$

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.

$- 5 x^{2} y^{3} z^{10} \to 15$

$6 x^{4} y^{5} z^{2} \to 11$

$3 x y^{5} \to 6$

The largest exponent is the degree of the polynomial.

$15$

Step 3

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

$- 5 x^{2} y^{3} z^{10}$

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.

$- 5 x^{2} y^{3} z^{10}$

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

$- 5$

Step 5

List the results.

Polynomial Degree: $15$

Leading Term: $- 5 x^{2} y^{3} z^{10}$

Leading Coefficient: $- 5$