Find the Degree, Leading Term, and Leading Coefficient -2x+3-5x^3+x^4

$- 2 x + 3 - 5 x^{3} + x^{4}$

Step 1

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

Move $3$ .

$- 2 x - 5 x^{3} + x^{4} + 3$

Move $- 2 x$ .

$- 5 x^{3} + x^{4} - 2 x + 3$

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

$x^{4} - 5 x^{3} - 2 x + 3$

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.

$x^{4} \to 4$

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

$- 2 x \to 1$

$3 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$x^{4}$

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.

$x^{4}$

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

$1$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $x^{4}$

Leading Coefficient: $1$