Find the Degree, Leading Term, and Leading Coefficient 2x^5-3x^4+12x^3-2

$2 x^{5} - 3 x^{4} + 12 x^{3} - 2$

Step 1

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.

$2 x^{5} \to 5$

$- 3 x^{4} \to 4$

$12 x^{3} \to 3$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$5$

Step 2

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

$2 x^{5}$

Step 3

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.

$2 x^{5}$

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

$2$

Step 4

List the results.

Polynomial Degree: $5$

Leading Term: $2 x^{5}$

Leading Coefficient: $2$