Find the Degree, Leading Term, and Leading Coefficient g(x)=x^4-1/3x^2+10-4x^3+2x

$g (x) = x^{4} - \frac{1}{3} x^{2} + 10 - 4 x^{3} + 2 x$

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

Combine $x^{2}$ and $\frac{1}{3}$ .

$g (x) = x^{4} - \frac{x^{2}}{3} + 10 - 4 x^{3} + 2 x$

Reorder.

Move $10$ .

$g (x) = x^{4} - \frac{x^{2}}{3} - 4 x^{3} + 2 x + 10$

Move $- \frac{x^{2}}{3}$ .

$g (x) = x^{4} - 4 x^{3} - \frac{x^{2}}{3} + 2 x + 10$

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.

$x^{4} \to 4$

$- 4 x^{3} \to 3$

$- \frac{x^{2}}{3} \to 2$

$2 x \to 1$

$10 \to 0$

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: $1$