Find the Degree, Leading Term, and Leading Coefficient h(x)=-5x+8x^2+x^3

$h (x) = - 5 x + 8 x^{2} + x^{3}$

Step 1

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

Move $- 5 x$ .

$h (x) = 8 x^{2} + x^{3} - 5 x$

Reorder $8 x^{2}$ and $x^{3}$ .

$h (x) = x^{3} + 8 x^{2} - 5 x$

Step 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.

$x^{3} \to 3$

$8 x^{2} \to 2$

$- 5 x \to 1$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$x^{3}$

Step 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.

$x^{3}$

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

$1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $x^{3}$

Leading Coefficient: $1$