Find the Degree, Leading Term, and Leading Coefficient f(x)=-4x^2+x^5+10x^3+5x+8x^4

$f (x) = - 4 x^{2} + x^{5} + 10 x^{3} + 5 x + 8 x^{4}$

Step 1

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

Move $5 x$ .

$f (x) = - 4 x^{2} + x^{5} + 10 x^{3} + 8 x^{4} + 5 x$

Move $- 4 x^{2}$ .

$f (x) = x^{5} + 10 x^{3} + 8 x^{4} - 4 x^{2} + 5 x$

Move $10 x^{3}$ .

$f (x) = x^{5} + 8 x^{4} + 10 x^{3} - 4 x^{2} + 5 x$

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.

$x^{5} \to 5$

$8 x^{4} \to 4$

$10 x^{3} \to 3$

$- 4 x^{2} \to 2$

$5 x \to 1$

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$x^{5}$

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.

$x^{5}$

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

$1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $x^{5}$

Leading Coefficient: $1$