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

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

Step 1

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

Move $- 3 x$ .

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

Reorder $4 x^{2}$ and $5 x^{3}$ .

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

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.

$5 x^{3} \to 3$

$4 x^{2} \to 2$

$- 3 x \to 1$

$- 7 \to 0$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$5 x^{3}$

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.

$5 x^{3}$

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

$5$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $5 x^{3}$

Leading Coefficient: $5$