Find the Degree, Leading Term, and Leading Coefficient 7+3x^2-5x^3+6x^2-2x

$7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$

Step 1

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

Add $3 x^{2}$ and $6 x^{2}$ .

$7 - 5 x^{3} + 9 x^{2} - 2 x$

Move $7$ .

$- 5 x^{3} + 9 x^{2} - 2 x + 7$

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.

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

$9 x^{2} \to 2$

$- 2 x \to 1$

$7 \to 0$

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: $- 5$