Find the Degree, Leading Term, and Leading Coefficient f(x)=x^4-5x^2-10x^3+6+10x

$f (x) = x^{4} - 5 x^{2} - 10 x^{3} + 6 + 10 x$

Step 1

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

Move $6$ .

$f (x) = x^{4} - 5 x^{2} - 10 x^{3} + 10 x + 6$

Move $- 5 x^{2}$ .

$f (x) = x^{4} - 10 x^{3} - 5 x^{2} + 10 x + 6$

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.

$x^{4} \to 4$

$- 10 x^{3} \to 3$

$- 5 x^{2} \to 2$

$10 x \to 1$

$6 \to 0$

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: $1$