Question 1083297
Set (x-1)(x+4) equal to zero and solve for x. The two solutions are x = 1 or x = -4. Plot -4 and 1 on the number line. Mark the regions between and around the points P, Q, and R as you see below
<img src = "https://i.imgur.com/4PSoNcW.png">
Pick a representative point from the red region P. One such value is x = -6. Plug this into the expression (x-1)(x+4) to get


(x-1)(x+4) = (-6-1)(-6+4) = (-7)*(-2) = 14


This result is positive, so (x-1)(x+4) > 0 for any point in the red region


--------------

Repeat for the blue region Q. Pick something like x = -2


(x-1)(x+4) = (-2-1)(-2+4) = (-3)*(2) = -6


So (x-1)(x+4) < 0 for the blue region

---------------

Repeat for the green region R
Pick something like x = 3


(x-1)(x+4) = (3-1)*(3+4) = (2)*(7) = 14

So (x-1)(x+4) > 0 for the green region

-----------------------------------

In summary, (x-1)(x+4) > 0 if you pick an x value from either the red region P or from the green region R

(x-1)(x+4) < 0 is true if you pick a point from the blue region Q

-----------------------------------

Note: plugging either x = -4 or x = 1 leads to (x-1)(x+4) being 0 so (x-1)(x+4) > 0 nor (x-1)(x+4) < 0 is true.