For which values of x is the value of ($x^2$ - 6x + 8) negative?

Explanation

A) 2 < x < 4. Factor first: $x^2$ − 6x + 8 = (x − 2)(x − 4). A product of two factors is negative only when they have opposite signs. That happens only between the roots, where x − 2 > 0 and x − 4 < 0. Outside that interval both factors share a sign, so the value is zero or positive.