Find the Maximum Number of Real Roots y=-x^6-6x^5+50x^3+45x^2-108x-108

$y = - x^{6} - 6 x^{5} + 50 x^{3} + 45 x^{2} - 108 x - 108$

Step 1

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

$- x^{6} \to 6$

$- 6 x^{5} \to 5$

$50 x^{3} \to 3$

$45 x^{2} \to 2$

$- 108 x \to 1$

$- 108 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$6$

Step 3

The maximum number of possible roots is the degree of $- x^{6} - 6 x^{5} + 50 x^{3} + 45 x^{2} - 108 x - 108$ .

$6$