Find the Degree, Leading Term, and Leading Coefficient P(x)=-3x^4+6x^3+x-5

$P (x) = - 3 x^{4} + 6 x^{3} + x - 5$

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.

$- 3 x^{4} \to 4$

$6 x^{3} \to 3$

$x \to 1$

$- 5 \to 0$

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.

$- 3 x^{4}$

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.

$- 3 x^{4}$

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

$- 3$

Step 4

List the results.

Polynomial Degree: $4$

Leading Term: $- 3 x^{4}$

Leading Coefficient: $- 3$