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 Question from Ron, a student: Hello I'm trying to find out the intervals where the function is positive and negative. It's for a polynomial function y= -(x+2)^2 (x-2) and y= (x+1)(x+4)(x-3) I have tried the right and left side of each x-intercepts, but I still don't understand the results thank you for your help

Hi Ron,

I want to illustrate with the function f(x) = -(1/4) (x - 1)2 (x + 2)3.

The x-intercepts are 1 and -2 and these two intercepts divide the line into three intervals.

To the left of -2 I chose x = -3. f(-3) = -(1/4) (-3 - 1)2 (-3 + 2)3 which is positive so the function is positive on the interval -∞ < x < -2.

Between -2 and 1 I chose x = 0. f(0) = -(1/4) (0 - 1)2 (0 + 2)3 which is negative so the function is negative on the interval -2 < x < 1.

To the right of 1 I chose x = 2. f(2) = -(1/4) (2 - 1)2 (2 + 2)3 which is negative so the function is negative on the interval 1 < x < ∞.

Here is a sketch of the function.

Penny

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