Find the Degree, Leading Term, and Leading Coefficient P(x)=4x^5+9x^4+6x^3-x^2+2x-7

$P (x) = 4 x^{5} + 9 x^{4} + 6 x^{3} - x^{2} + 2 x - 7$

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.

$4 x^{5} \to 5$

$9 x^{4} \to 4$

$6 x^{3} \to 3$

$- x^{2} \to 2$

$2 x \to 1$

$- 7 \to 0$

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.

$4 x^{5}$

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.

$4 x^{5}$

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

$4$

Step 4

List the results.

Polynomial Degree: $5$

Leading Term: $4 x^{5}$

Leading Coefficient: $4$