Find the Degree, Leading Term, and Leading Coefficient f(x)=2x^4-5x^3+3x^2+7x-1

$f (x) = 2 x^{4} - 5 x^{3} + 3 x^{2} + 7 x - 1$

Step 1

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.

$2 x^{4} \to 4$

$- 5 x^{3} \to 3$

$3 x^{2} \to 2$

$7 x \to 1$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 2

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

$2 x^{4}$

Step 3

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.

$2 x^{4}$

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

$2$

Step 4

List the results.

Polynomial Degree: $4$

Leading Term: $2 x^{4}$

Leading Coefficient: $2$