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

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

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

Move $6$ .

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

Move $6 x$ .

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

Move $4 x^{2}$ .

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

Reorder $7 x^{3}$ and $- x^{4}$ .

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

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.

$- x^{4} \to 4$

$7 x^{3} \to 3$

$4 x^{2} \to 2$

$6 x \to 1$

$6 \to 0$

The largest exponent is the degree of the polynomial.

$4$

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

$- x^{4}$

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.

$- x^{4}$

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

$- 1$

List the results.

Polynomial Degree: $4$

Leading Term: $- x^{4}$

Leading Coefficient: $- 1$