Find the Degree, Leading Term, and Leading Coefficient f(x)=-3x+5x^3-6x^2+2

$f (x) = - 3 x + 5 x^{3} - 6 x^{2} + 2$

Step 1

Move $- 3 x$ .

$f (x) = 5 x^{3} - 6 x^{2} - 3 x + 2$

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.

$5 x^{3} \to 3$

$- 6 x^{2} \to 2$

$- 3 x \to 1$

$2 \to 0$

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: $5$