Find the Degree, Leading Term, and Leading Coefficient f(x)=7x-8x^5-2+9x^2+2x^7

$f (x) = 7 x - 8 x^{5} - 2 + 9 x^{2} + 2 x^{7}$

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

Move $- 2$ .

$f (x) = 7 x - 8 x^{5} + 9 x^{2} + 2 x^{7} - 2$

Move $7 x$ .

$f (x) = - 8 x^{5} + 9 x^{2} + 2 x^{7} + 7 x - 2$

Move $9 x^{2}$ .

$f (x) = - 8 x^{5} + 2 x^{7} + 9 x^{2} + 7 x - 2$

Reorder $- 8 x^{5}$ and $2 x^{7}$ .

$f (x) = 2 x^{7} - 8 x^{5} + 9 x^{2} + 7 x - 2$

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.

$2 x^{7} \to 7$

$- 8 x^{5} \to 5$

$9 x^{2} \to 2$

$7 x \to 1$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$7$

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

$2 x^{7}$

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.

$2 x^{7}$

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

$2$

List the results.

Polynomial Degree: $7$

Leading Term: $2 x^{7}$

Leading Coefficient: $2$