Find the Degree, Leading Term, and Leading Coefficient f(x)=2-11x+2x^2

$f (x) = 2 - 11 x + 2 x^{2}$

Step 1

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

Move $2$ .

$f (x) = - 11 x + 2 x^{2} + 2$

Reorder $- 11 x$ and $2 x^{2}$ .

$f (x) = 2 x^{2} - 11 x + 2$

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.

$2 x^{2} \to 2$

$- 11 x \to 1$

$2 \to 0$

The largest exponent is the degree of the polynomial.

$2$

Step 3

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

$2 x^{2}$

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.

$2 x^{2}$

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

$2$

Step 5

List the results.

Polynomial Degree: $2$

Leading Term: $2 x^{2}$

Leading Coefficient: $2$