Find the Degree, Leading Term, and Leading Coefficient h(x)=5/3x^2- square root of 7x^4+8x^3-1/2+x

$h (x) = \frac{5}{3} x^{2} - \sqrt{7} x^{4} + 8 x^{3} - \frac{1}{2} + x$

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

Combine $\frac{5}{3}$ and $x^{2}$ .

$h (x) = \frac{5 x^{2}}{3} - \sqrt{7} x^{4} + 8 x^{3} - \frac{1}{2} + x$

Reorder.

Move $- \frac{1}{2}$ .

$h (x) = \frac{5 x^{2}}{3} - \sqrt{7} x^{4} + 8 x^{3} + x - \frac{1}{2}$

Move $\frac{5 x^{2}}{3}$ .

$h (x) = - \sqrt{7} x^{4} + 8 x^{3} + \frac{5 x^{2}}{3} + x - \frac{1}{2}$

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.

$- \sqrt{7} x^{4} \to 4$

$8 x^{3} \to 3$

$\frac{5 x^{2}}{3} \to 2$

$x \to 1$

$- \frac{1}{2} \to 0$

The largest exponent is the degree of the polynomial.

$4$

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

$- \sqrt{7} x^{4}$

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.

$- \sqrt{7} x^{4}$

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

$- 1$

List the results.

Polynomial Degree: $4$

Leading Term: $- \sqrt{7} x^{4}$

Leading Coefficient: $- 1$