Find the Degree, Leading Term, and Leading Coefficient f(x)=5x-2x^2+9x^3+10x^4-2

$f (x) = 5 x - 2 x^{2} + 9 x^{3} + 10 x^{4} - 2$

Step 1

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

Move $5 x$ .

$f (x) = - 2 x^{2} + 9 x^{3} + 10 x^{4} + 5 x - 2$

Move $- 2 x^{2}$ .

$f (x) = 9 x^{3} + 10 x^{4} - 2 x^{2} + 5 x - 2$

Reorder $9 x^{3}$ and $10 x^{4}$ .

$f (x) = 10 x^{4} + 9 x^{3} - 2 x^{2} + 5 x - 2$

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.

$10 x^{4} \to 4$

$9 x^{3} \to 3$

$- 2 x^{2} \to 2$

$5 x \to 1$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$10 x^{4}$

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.

$10 x^{4}$

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

$10$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $10 x^{4}$

Leading Coefficient: $10$