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

$f (x) = 9 x^{4} - 8 x + x^{5} + 3 x^{2}$

Step 1

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

Move $- 8 x$ .

$f (x) = 9 x^{4} + x^{5} + 3 x^{2} - 8 x$

Reorder $9 x^{4}$ and $x^{5}$ .

$f (x) = x^{5} + 9 x^{4} + 3 x^{2} - 8 x$

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.

$x^{5} \to 5$

$9 x^{4} \to 4$

$3 x^{2} \to 2$

$- 8 x \to 1$

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.

$x^{5}$

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.

$x^{5}$

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

$1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $x^{5}$

Leading Coefficient: $1$