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

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

Step 1

Reorder $4 x^{4}$ and $- 8 x^{6}$ .

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

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.

$- 8 x^{6} \to 6$

$4 x^{4} \to 4$

$6 x^{3} \to 3$

$- 4 \to 0$

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.

$- 8 x^{6}$

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.

$- 8 x^{6}$

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

$- 8$

Step 5

List the results.

Polynomial Degree: $6$

Leading Term: $- 8 x^{6}$

Leading Coefficient: $- 8$