SOLUTION: If f(x) = x(x + 1)(x - 4), use interval notation to give all values of x where f(x)> 0.

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Question 82567: If f(x) = x(x + 1)(x - 4), use interval notation to give all values of x where f(x)> 0.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x(x + 1)(x - 4)
Zeros (x - intercepts)
x = 0
x = -1
x = 4
f(x) > 0
x(x + 1)(x - 4) > 0
X-Axis
<---------(-1)-------(0)-------------------(4)--------------->
Test: x = -2
(-2)(-2 + 1)(-2 - 4) > 0
(-2)(-1)(-6) > 0
-12 > 0 False
Test: x = -0.5
(-0.5)(-0.5 + 1)(-0.5 - 4) > 0
(-0.5)(0.5)(-4.5) > 0
1.125 > 0 True
Test: x = 1
(1)(1 + 1)(1 - 4) > 0
(1)(2)(-3) > 0
-6 > 0 False
Test: x = 5
(5)(5 + 1)(5 - 4) > 0
(5)(6)(1) > 0
30 > 0 True
X-Axis
<---------(-1)========(0)-------------------(4)==============>
(-1,0)U(4,+infinity)
Proof:
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3+-+4x%5E2+%2B+x%5E2+-+4x%29