Find the Degree, Leading Term, and Leading Coefficient 3x^3+x^2-8x^5+2x^3-4x

$3 x^{3} + x^{2} - 8 x^{5} + 2 x^{3} - 4 x$

Step 1

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

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

$5 x^{3} + x^{2} - 8 x^{5} - 4 x$

Simplify the expression.

Move $x^{2}$ .

$5 x^{3} - 8 x^{5} + x^{2} - 4 x$

Reorder $5 x^{3}$ and $- 8 x^{5}$ .

$- 8 x^{5} + 5 x^{3} + x^{2} - 4 x$

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.

$- 8 x^{5} \to 5$

$5 x^{3} \to 3$

$x^{2} \to 2$

$- 4 x \to 1$

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.

$- 8 x^{5}$

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.

$- 8 x^{5}$

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

$- 8$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- 8 x^{5}$

Leading Coefficient: $- 8$