Which are the solutions to the inequality (x-3)(x+5)< _0

[ - 5, 3 ]

Step-by-step explanation:

Solve (x - 3)(x + 5) = 0

The zeros are x = - 5 and x = 3

These divide the domain into 3 intervals

(- ∞, - 5 ], [- 5, 3 ], [ 3, + ∞ )

Choose a test point in each interval and consider the sign of the result.

x = - 10 : (- 10 - 3)(- 10 + 5) = (- 13)(- 5) = 65 > 0

x = 0 : (0 - 3)(0 + 5) = (- 3)(5) = - 15 < 0 ← required result

x = 5 : (5 - 3)(5 + 5) = (2)(10) = 20 > 0

The solution is [ - 5, 3 ] or - 5 ≤ x ≤ 3

3x^3-x^2+6x-9