Precalc question

Question

Use the cut-point method to find the solution set of the following inequality: (x + 4)(x – 5)(4x + 1) ≥ 0. What are the cut points?

1. -4, 5, 1/4
2. -4, 5, -1/4
3. -4, -5, -1/4
4. -4, -5, 1/4

Answer 1

The cut-points are the points there the expression (x + 4)(x – 5)(4x + 1) changes the sign. We find these points solving

x + 4 = 0 or x = -4,

x – 5 = 0 or x = 5,

4x + 1 = 0 or x = -1/4.

Hence, 2 is the right answer.