Find the Degree, Leading Term, and Leading Coefficient f(x)=1/2x^2+8-5x^3-19x

$f (x) = \frac{1}{2} x^{2} + 8 - 5 x^{3} - 19 x$

Step 1

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

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

$f (x) = \frac{x^{2}}{2} + 8 - 5 x^{3} - 19 x$

Simplify the expression.

Move $8$ .

$f (x) = \frac{x^{2}}{2} - 5 x^{3} - 19 x + 8$

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

$f (x) = - 5 x^{3} + \frac{x^{2}}{2} - 19 x + 8$

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.

$- 5 x^{3} \to 3$

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

$- 19 x \to 1$

$8 \to 0$

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.

$- 5 x^{3}$

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.

$- 5 x^{3}$

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

$- 5$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- 5 x^{3}$

Leading Coefficient: $- 5$