Look at #(x + 1)(x - 3) = 0
This means that the function is 0 at x = -1 and x = 3x=−1andx=3.
Also, it means that the sign of the corresponding factor changes sign at that value of x.
At values of x < -1:
Both (x + 1)(x+1) and (x - 3)(x−3) are negative. A negative multiplied by a negative is a positive, therefore, x < -1 is one of the regions where (x + 1)(x - 3) > 0(x+1)(x−3)>0. Let's make a note of that:
x < -1x<−1
At values between -1 and 3:
(x + 1)(x+1) is positive but (x -3)(x−3) is still negative. A positive multiplied by a negative is negative, therefore, this is NOT a region for (x + 1)(x - 3) >0(x+1)(x−3)>0
At values x > 3x>3:
Both (x + 1)(x+1) and (x - 3)(x−3) are positive. A positive multiplied by a positive is a positive, therefore, x > 3 is one of the regions where #(x + 1)(x - 3) > 0. Let's make a note of that:
x < -1 and x > 3x<−1andx>3
We have no more regions to investigate, therefore, the above is our answer.
