Final answer:
To solve the polynomial inequality (x+1)(x-3)^(2) > 0, find the critical points, determine the regions where the polynomial is positive or negative, and evaluate test values to find the solution.
Step-by-step explanation:
To solve the inequality (x+1)(x-3)^(2) > 0, we first need to find the critical points where the expression equals zero. These critical points are x = -1 and x = 3. Since the inequality is greater than zero, we are looking for the regions where the polynomial is positive. We can test these regions by picking test values within each region and checking if the expression is positive or negative. From this, we can determine the solution to be x < -1 or -1 < x < 3.