Find the Degree, Leading Term, and Leading Coefficient -1+6x+x^2+4x^4

$- 1 + 6 x + x^{2} + 4 x^{4}$

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

Move $- 1$ .

$6 x + x^{2} + 4 x^{4} - 1$

Move $6 x$ .

$x^{2} + 4 x^{4} + 6 x - 1$

Reorder $x^{2}$ and $4 x^{4}$ .

$4 x^{4} + x^{2} + 6 x - 1$

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.

$4 x^{4} \to 4$

$x^{2} \to 2$

$6 x \to 1$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$4$

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

$4 x^{4}$

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.

$4 x^{4}$

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

$4$

List the results.

Polynomial Degree: $4$

Leading Term: $4 x^{4}$

Leading Coefficient: $4$