Find the Degree, Leading Term, and Leading Coefficient f(x)=-x^5+6x^7-7x^3-2-6x^2

$f (x) = - x^{5} + 6 x^{7} - 7 x^{3} - 2 - 6 x^{2}$

Step 1

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

Move $- 2$ .

$f (x) = - x^{5} + 6 x^{7} - 7 x^{3} - 6 x^{2} - 2$

Reorder $- x^{5}$ and $6 x^{7}$ .

$f (x) = 6 x^{7} - x^{5} - 7 x^{3} - 6 x^{2} - 2$

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.

$6 x^{7} \to 7$

$- x^{5} \to 5$

$- 7 x^{3} \to 3$

$- 6 x^{2} \to 2$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$7$

Step 3

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

$6 x^{7}$

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.

$6 x^{7}$

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

$6$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $6 x^{7}$

Leading Coefficient: $6$