Find the Maximum Number of Real Roots f(x)=-x^5-4x^3-5x+6

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

Step 1

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

$- x^{5} \to 5$

$- 4 x^{3} \to 3$

$- 5 x \to 1$

$6 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The maximum number of possible roots is the degree of $- x^{5} - 4 x^{3} - 5 x + 6$ .

$5$