Find the Degree, Leading Term, and Leading Coefficient 15x^3y^2z-6xy^5z^8+4x

$15 x^{3} y^{2} z - 6 x y^{5} z^{8} + 4 x$

Step 1

Reorder $15 x^{3} y^{2} z$ and $- 6 x y^{5} z^{8}$ .

$- 6 x y^{5} z^{8} + 15 x^{3} y^{2} z + 4 x$

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.

$- 6 x y^{5} z^{8} \to 14$

$15 x^{3} y^{2} z \to 6$

$4 x \to 1$

The largest exponent is the degree of the polynomial.

$14$

Step 3

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

$- 6 x y^{5} z^{8}$

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.

$- 6 x y^{5} z^{8}$

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

$- 6$

Step 5

List the results.

Polynomial Degree: $14$

Leading Term: $- 6 x y^{5} z^{8}$

Leading Coefficient: $- 6$