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

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

Step 1

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

Move $5 x$ .

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

Reorder $- x^{3}$ and $3 x^{5}$ .

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

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.

$3 x^{5} \to 5$

$- x^{3} \to 3$

$5 x \to 1$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$3 x^{5}$

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.

$3 x^{5}$

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

$3$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $3 x^{5}$

Leading Coefficient: $3$