Find the Degree, Leading Term, and Leading Coefficient 5x^5+8x^2+2x-3x^9-8x^4-4x^5

$5 x^{5} + 8 x^{2} + 2 x - 3 x^{9} - 8 x^{4} - 4 x^{5}$

Step 1

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

Subtract $4 x^{5}$ from $5 x^{5}$ .

$x^{5} + 8 x^{2} + 2 x - 3 x^{9} - 8 x^{4}$

Simplify the expression.

Move $2 x$ .

$x^{5} + 8 x^{2} - 3 x^{9} - 8 x^{4} + 2 x$

Move $8 x^{2}$ .

$x^{5} - 3 x^{9} - 8 x^{4} + 8 x^{2} + 2 x$

Reorder $x^{5}$ and $- 3 x^{9}$ .

$- 3 x^{9} + x^{5} - 8 x^{4} + 8 x^{2} + 2 x$

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.

$- 3 x^{9} \to 9$

$x^{5} \to 5$

$- 8 x^{4} \to 4$

$8 x^{2} \to 2$

$2 x \to 1$

The largest exponent is the degree of the polynomial.

$9$

Step 3

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

$- 3 x^{9}$

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.

$- 3 x^{9}$

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

$- 3$

Step 5

List the results.

Polynomial Degree: $9$

Leading Term: $- 3 x^{9}$

Leading Coefficient: $- 3$