Find the Degree, Leading Term, and Leading Coefficient 8x^5-12x^6+14x^3-9

$8 x^{5} - 12 x^{6} + 14 x^{3} - 9$

Step 1

Reorder $8 x^{5}$ and $- 12 x^{6}$ .

$- 12 x^{6} + 8 x^{5} + 14 x^{3} - 9$

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.

$- 12 x^{6} \to 6$

$8 x^{5} \to 5$

$14 x^{3} \to 3$

$- 9 \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 3

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

$- 12 x^{6}$

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.

$- 12 x^{6}$

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

$- 12$

Step 5

List the results.

Polynomial Degree: $6$

Leading Term: $- 12 x^{6}$

Leading Coefficient: $- 12$