Determine the solution set for the polynomial inequality $x(x + 4)(x - 2)(x - 5) \leq 0$.

$(-\infty, -4] \cup [0, 2] \cup [5, \infty)$

$(-\infty, -4) \cup (0, 2) \cup (5, \infty)$

Beyond Quadratics Practice — Grade 4 amc_math

Lesson 15.2: Beyond Quadratics — Practice Questions

1. What is the solution set for the inequality $(x + 1)(x - 2)(x - 4) < 0$?
- A. $(-\infty, -1) \cup (2, 4)$
- B. $(-1, 2) \cup (4, \infty)$
- C. $(-\infty, -1] \cup [2, 4]$
- D. $[-1, 2] \cup [4, \infty)$
2. Find the solution set for the inequality $(x - 3)(x + 2)^2 > 0$. Express your answer in interval notation: ___.
3. Determine the solution set for the polynomial inequality $x(x + 4)(x - 2)(x - 5) \leq 0$.
- A. $[-4, 0] \cup [2, 5]$
- B. $(-\infty, -4] \cup [0, 2] \cup [5, \infty)$
- C. $(-4, 0) \cup (2, 5)$
- D. $(-\infty, -4) \cup (0, 2) \cup (5, \infty)$
4. Solve the inequality $(3x - 1)(x + 2)(x - 4) > 0$. Express the solution in interval notation. The solution is ___.
5. Which of the following is part of the solution set for the inequality $x(x - 5)(x + 3)^2 \leq 0$?
- A. $[-3, 0]$
- B. $[0, 5]$
- C. $(5, \infty)$
- D. $(-\infty, -3)$
6. Find the solution set for the inequality $(x+1)(x-2)(x-5) > 0$.
- A. (-∞, -1) U (2, 5)
- B. (-1, 2) U (5, ∞)
- C. (-∞, -1) U (5, ∞)
- D. (-1, 5)
7. Solve the inequality $\frac{(x+4)(x-1)}{x-3} \geq 0$. Express your answer in interval notation: ___.
8. What is the solution set for the inequality $(x+4)(x-2)^2(x-5) \geq 0$?
- A. [-4, 5]
- B. (-∞, -4] U [5, ∞)
- C. (-∞, -4] U {2} U [5, ∞)
- D. [-4, 2] U [5, ∞)
9. Find the solution set for the rational inequality $\frac{x-3}{(x+2)(x-5)} < 0$. Write your answer in interval notation: ___.
10. When solving an inequality of the form $(x-3)^2 P(x) \leq 0$, how does the point $x=3$ affect the solution set?
- A. x=3 must be excluded because division by zero is undefined.
- B. x=3 is always included because the expression equals zero there.
- C. x=3 is only included if P(3) is negative.
- D. x=3 has no effect on the solution set.