QuestionFactor the following function: $x^{4}+3 x^{3}-15 x^{2}-19 x+30$. How many real-valued roots does this polynomial have?

Studdy Solution
The complete factorization of the polynomial is:
$$(x - 1)(x + 2)(x - 3)(x + 5)$$
Each factor corresponds to a real root. The roots are $x = 1, x = -2, x = 3, x = -5$.
The polynomial has $\boxed{4}$ real-valued roots.