# How do you find the number of roots for x^3 - 3x^2 - 18x - 176 = 0 using the fundamental theorem of algebra?

Apr 5, 2016

Since the function's degree is $3$, it has $3$ roots.

#### Explanation:

The Fundamental Theorem of Algebra (FTOA), for a polynomial function such as ${x}^{3} - 3 {x}^{2} - 18 x - 176 = 0$, states that the degree of the polynomial function is equivalent to the function's number of roots.

The degree of a function is the highest exponent on any of its terms, which in this case is the $3$ in the exponent of ${x}^{3}$.

Since this function has degree $3$, the FTOA states that it will have three roots.

graph{x^3-3x^2-18x-176 [-10, 15, -300, 70]}

Graphing the function, it appears to have only one root (zero) at $x = 8$, but it has $2$ more complex roots for a total of $3$ roots.