Find the Degree, Leading Term, and Leading Coefficient f(x)=10x^2-5x+5x^3-x^4

$f (x) = 10 x^{2} - 5 x + 5 x^{3} - x^{4}$

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

Move $- 5 x$ .

$f (x) = 10 x^{2} + 5 x^{3} - x^{4} - 5 x$

Move $10 x^{2}$ .

$f (x) = 5 x^{3} - x^{4} + 10 x^{2} - 5 x$

Reorder $5 x^{3}$ and $- x^{4}$ .

$f (x) = - x^{4} + 5 x^{3} + 10 x^{2} - 5 x$

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.

$- x^{4} \to 4$

$5 x^{3} \to 3$

$10 x^{2} \to 2$

$- 5 x \to 1$

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: $- 1$