Find the Degree, Leading Term, and Leading Coefficient 2f^3+2f-8f^2+12f^4

$2 f^{3} + 2 f - 8 f^{2} + 12 f^{4}$

Step 1

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

Move $2 f$ .

$2 f^{3} - 8 f^{2} + 12 f^{4} + 2 f$

Move $- 8 f^{2}$ .

$2 f^{3} + 12 f^{4} - 8 f^{2} + 2 f$

Reorder $2 f^{3}$ and $12 f^{4}$ .

$12 f^{4} + 2 f^{3} - 8 f^{2} + 2 f$

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.

$12 f^{4} \to 4$

$2 f^{3} \to 3$

$- 8 f^{2} \to 2$

$2 f \to 1$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$12 f^{4}$

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.

$12 f^{4}$

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

$12$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $12 f^{4}$

Leading Coefficient: $12$