Question 44533
If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. 

THE ROOTS ARE 0,-3,1.....-3,0,1 IN INCREASING ORDER
PLACE THE ROOTS ON A NUMBER LINE AS SHOWN BELOW

....<-3.......-3...........0........1.......>1....IN INCREASING ORDER.
NOW COME FROM RIGHT MOST
ZONE 1.....>1...THAT IS BEYOND THE LARGEST ROOT ..F(X) WILL BE +VE
ZONE 2.....BETWEEN 0 AND 1.........................F(X) WILL BE -VE
ZONE 3.....BETWEEN -3 AND 1..................... ..F(X) WILL BE +VE
ZONE 4.....<-3.....................................F(X) WILL BE -VE
HENCE F(X)>0 IN INTERVALS
X>1 THAT IS  (1,INFINITY) AND -3<X<1...THAT IS (-3,1)