Find the Degree, Leading Term, and Leading Coefficient f(x)=3-10x+5x^4+5x^2+8x^7

$f (x) = 3 - 10 x + 5 x^{4} + 5 x^{2} + 8 x^{7}$

Step 1

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

Move $3$ .

$f (x) = - 10 x + 5 x^{4} + 5 x^{2} + 8 x^{7} + 3$

Move $- 10 x$ .

$f (x) = 5 x^{4} + 5 x^{2} + 8 x^{7} - 10 x + 3$

Move $5 x^{2}$ .

$f (x) = 5 x^{4} + 8 x^{7} + 5 x^{2} - 10 x + 3$

Reorder $5 x^{4}$ and $8 x^{7}$ .

$f (x) = 8 x^{7} + 5 x^{4} + 5 x^{2} - 10 x + 3$

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.

$8 x^{7} \to 7$

$5 x^{4} \to 4$

$5 x^{2} \to 2$

$- 10 x \to 1$

$3 \to 0$

The largest exponent is the degree of the polynomial.

$7$

Step 3

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

$8 x^{7}$

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.

$8 x^{7}$

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

$8$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $8 x^{7}$

Leading Coefficient: $8$