The interval where f(x) = –2(x + 2)(x – 3)(x – 1) is positive will be

The interval where f(x) = –2(x + 2)(x – 3)(x – 1) is positive will be
A. x > 0
B. –2 < x < 1, x > 3
C. x < –2, 1 < x < 3
D. x < 0

I know the point where x-intercepts is (-2,0) (1,0) (3,0) But I need help with how to figure out the domain. I believe the answer is B based off the graph I get, but can someone explain to me why it wouldn't be C?

The possible intervals are -infinity
Choose any value from each interval and substitute into the equation to see if it is positive or negative.

For x = -3, f(-3) is positive, so f(x) is positive for -infinity
For x = 0, f(0) is negative so f(x) is negative for -2
For x = 2, f(2) is positive so f(x) is positive for 1
For x = 5, f(5) is negative, so f(x) is negative for 33

The correct answer is C..

Answer is (C)..

Use wavy curve method..
f(x) = 0 at x ∈ {-2,1,3}

Thus, mark out these points on number line and see the sign scheme. Remember the leading coefficient is Negative here.

Thus f(x)<0 ∀ x ∈ (-2,1) ⋃ (3,∞)

and f(x)>0 ∀ x ∈ (-∞,-2) ⋃ (1,3)