Question

Consider the function .

For which intervals is f(x) positive? Check all that apply.

(–∞, –3)
(–3, –2)
(–2, 2)
(2, 3)
(∞, 3)

Answer 1

You likely mean f(x) = (x+3)(x+2)(x-2)(x-3) (zeros at -3, -2, 2, 3). Checking signs on each interval gives:

- (-∞, -3): all four factors negative → product positive
- (-3, -2): one factor positive, three negative → product negative
- (-2, 2): two factors positive, two negative → product positive
- (2, 3): three factors positive, one negative → product negative
- (3, ∞): all factors positive → product positive

So f(x) > 0 on (-∞, -3), (-2, 2), and (3, ∞).