Polynomial Inequalities

Question

Solve following polynomial inequalities. Show number line test and state your answers in interval notation

(step by step)

1) (x-5) (x+2) < 0

Answer 1

For the product to be less than zero one of the factors must be negative and the other factor must be positive

If x - 5 < 0, then x < 5 and x + 2 > 0 or x >-2

If s + 2 < 0, then x < -2 and x - 5 > 0 or x > 5

So x ∈ ℜ - {-2, 5}