Final answer:
To solve the inequality (x³ + 8x² < 0), factoring out x² gives x²(x + 8) < 0. Since x² is always non-negative, the expression is negative when x < -8, excluding zero as a solution. Hence, the answer is A. (x < -8).
Step-by-step explanation:
To solve the inequality (x³ + 8x² < 0) algebraically, we would look for values of x that make the expression negative. One way to do this is to factor the left-hand side of the inequality if possible. In our case, we can factor out an x², which gives us x²(x + 8) < 0. The inequality will hold true when either x² or (x + 8) is negative, but not both.
Since x² is always non-negative (zero or positive), the entire expression is negative when (x + 8) is negative, which is when x < -8. However, at x = 0, the x² term will make the entire expression equal to zero, which is not less than zero. So, we disregard x = 0 as a solution. Therefore, we conclude that the solution to the inequality is (x < -8). It is important to exclude zero since when x is zero, the inequality would not hold.
The correct answer is A. (x < -8).