(x+1)(x−2)(x−4)≤0
A)
(−1, 2) ∪ (4, ∞)
B)
(−∞, −1] ∪ [2, 4]
C)
[−1, 2] ∪ [4, ∞)
D)
(−∞, −1) ∪ (2, 4)
im confused on which to chose ( or ]
here is how I do these ...
Since it is already factored we can say that the critical values are: -1,2, and 4
so we have 4 sections on the number line:
1. ≤ -1
2. between -1 and 2
3. between 2 and 4
4. ≥ 4
I then pick a nice number for each section.
We don' actually have to calculate, just get the + or - results
1. how about x = -5
-(-)(-) ---> - so OK
2. how about x=0
+(-)(-) ---> = + , no
3. how about x = 3
+(+)(-) ---> - , oK
4. how about x = 5
+(+)(+) = + , no no
so our values are :
x≤-1, 2≤x≤4
I don't use the given notation, I will leave it up to you which of the given fits my old-fashioned but very clear notation.
check:
let y = (x+1)(x−2)(x−4)
which parts of the graph fall below the x-axis ?
http://www.wolframalpha.com/input/?i=y+%3D+%28x%2B1%29%28x%E2%88%922%29%28x%E2%88%924%29