Question 1126318
<br>
{{{f(x) = (x-2)(x+4)^2 = (x-2)(x+4)(x+4)}}}<br>
The function value is 0 when any of the factors is 0 -- at x=-4 and at x=2.  The function value can change sign only at those two values.  So...<br>
(1) On (-infinity,-4), all three factors are negative, so the function value is negative.
(2) On (-4,2) only one factor is negative, so the function value is again negative. (Both factors of (x+4) change sign at x=-4, so the function value remains negative.)
(4) On (2,infinity) all three factors are positive, so the function value is positive. (At x=2, only one factor changes sign, so the function value changes sign.)<br>
So....<br>
ANSWERS:
a. The roots are -4 and 2
b. The function value is positive only on (2,infinity)
c. The function value is negative on (-infinity,-4) U (-4,2)