Find the Degree, Leading Term, and Leading Coefficient g(t)=5t^5-2t^3+7t

$g (t) = 5 t^{5} - 2 t^{3} + 7 t$

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.

$5 t^{5} \to 5$

$- 2 t^{3} \to 3$

$7 t \to 1$

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.

$5 t^{5}$

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.

$5 t^{5}$

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

$5$

Step 4

List the results.

Polynomial Degree: $5$

Leading Term: $5 t^{5}$

Leading Coefficient: $5$