f(x) = x + 5 (x − 1)(x − 4) f(x) > 0 when x is in ?

Answer 1

x+5(x-1)(x-4)

=x+5(x^2-5x+4)

= 5x^2-24x+20=0

use the quadratic formula

x =2.4 +/- (1/10)sqr(176)

x= about 15.67, -11.27

f(x)>0

when x<-11.27 or x>15.67

when x is an element of (-inf,-11.27)U(15.67, inf)

UNLESS by chance you meant to write

f(x) = (x+5)(x-1)(x-4)

then it gets a little more complicated as

the intervals involved are (-inf, -5), (-5,1), (1,4), (4, inf)

x changes sign as it changes from one interval to the next

f(x)>0 when x is in (-5,1)U(4, inf)