Find the Degree, Leading Term, and Leading Coefficient f(x)=4x^2+x-8x^3+6x^7-1

$f (x) = 4 x^{2} + x - 8 x^{3} + 6 x^{7} - 1$

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

Move $x$ .

$f (x) = 4 x^{2} - 8 x^{3} + 6 x^{7} + x - 1$

Move $4 x^{2}$ .

$f (x) = - 8 x^{3} + 6 x^{7} + 4 x^{2} + x - 1$

Reorder $- 8 x^{3}$ and $6 x^{7}$ .

$f (x) = 6 x^{7} - 8 x^{3} + 4 x^{2} + x - 1$

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.

$6 x^{7} \to 7$

$- 8 x^{3} \to 3$

$4 x^{2} \to 2$

$x \to 1$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$7$

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

$6 x^{7}$

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.

$6 x^{7}$

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

$6$

List the results.

Polynomial Degree: $7$

Leading Term: $6 x^{7}$

Leading Coefficient: $6$