Find the Degree, Leading Term, and Leading Coefficient 9x^3+3x^8+6x^7+5x^6-7x^5

$9 x^{3} + 3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5}$

Step 1

Move $9 x^{3}$ .

$3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5} + 9 x^{3}$

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.

$3 x^{8} \to 8$

$6 x^{7} \to 7$

$5 x^{6} \to 6$

$- 7 x^{5} \to 5$

$9 x^{3} \to 3$

The largest exponent is the degree of the polynomial.

$8$

Step 3

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

$3 x^{8}$

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.

$3 x^{8}$

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

$3$

Step 5

List the results.

Polynomial Degree: $8$

Leading Term: $3 x^{8}$

Leading Coefficient: $3$