Find the Degree, Leading Term, and Leading Coefficient P(x)=-4x^3+10x^2+1

$P (x) = - 4 x^{3} + 10 x^{2} + 1$

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.

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

$10 x^{2} \to 2$

$1 \to 0$

The largest exponent is the degree of the polynomial.

$3$

Step 2

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

$- 4 x^{3}$

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.

$- 4 x^{3}$

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

$- 4$

Step 4

List the results.

Polynomial Degree: $3$

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

Leading Coefficient: $- 4$