Find the Degree, Leading Term, and Leading Coefficient f(x) = square root of 2x^5-7x^2-8x

$f (x) = \sqrt{2} x^{5} - 7 x^{2} - 8 x$

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.

$\sqrt{2} x^{5} \to 5$

$- 7 x^{2} \to 2$

$- 8 x \to 1$

The largest exponent is the degree of the polynomial.

$5$

Step 2

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

$\sqrt{2} x^{5}$

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.

$\sqrt{2} x^{5}$

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

$1$

Step 4

List the results.

Polynomial Degree: $5$

Leading Term: $\sqrt{2} x^{5}$

Leading Coefficient: $1$