Find the Maximum Number of Real Roots x^5-9x^4+13x^3+57x^2-86x-120

$x^{5} - 9 x^{4} + 13 x^{3} + 57 x^{2} - 86 x - 120$

Step 1

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

$x^{5} \to 5$

$- 9 x^{4} \to 4$

$13 x^{3} \to 3$

$57 x^{2} \to 2$

$- 86 x \to 1$

$- 120 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The maximum number of possible roots is the degree of $x^{5} - 9 x^{4} + 13 x^{3} + 57 x^{2} - 86 x - 120$ .

$5$