Find the Degree, Leading Term, and Leading Coefficient 5x^4-2x^2+1

$5 x^{4} - 2 x^{2} + 1$

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.

$5 x^{4} \to 4$

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

$1 \to 0$

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.

$5 x^{4}$

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.

$5 x^{4}$

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

$5$

Step 4

List the results.

Polynomial Degree: $4$

Leading Term: $5 x^{4}$

Leading Coefficient: $5$