Find the Maximum Number of Real Roots f(x)=-8x-x^4

$f (x) = - 8 x - x^{4}$

Step 1

Reorder $- 8 x$ and $- x^{4}$ .

$f (x) = - x^{4} - 8 x$

Step 2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- x^{4} \to 4$

$- 8 x \to 1$

Step 3

The largest exponent is the degree of the polynomial.

$4$

Step 4

The maximum number of possible roots is the degree of $- x^{4} - 8 x$ .

$4$