Question

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

Answer 1

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^3-3x^2-18x-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.