Find the Degree, Leading Term, and Leading Coefficient 3x^2+2x^4-7x^5+3

$3 x^{2} + 2 x^{4} - 7 x^{5} + 3$

Step 1

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

Move $3 x^{2}$ .

$2 x^{4} - 7 x^{5} + 3 x^{2} + 3$

Reorder $2 x^{4}$ and $- 7 x^{5}$ .

$- 7 x^{5} + 2 x^{4} + 3 x^{2} + 3$

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.

$- 7 x^{5} \to 5$

$2 x^{4} \to 4$

$3 x^{2} \to 2$

$3 \to 0$

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.

$- 7 x^{5}$

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.

$- 7 x^{5}$

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

$- 7$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- 7 x^{5}$

Leading Coefficient: $- 7$