For time t> =0, the velocity of a particle moving along the x-axis is given by v(t) = (t-5)(t-2)^2. at what values of t is the acceleration of the particle equal to 0? (a) 2 only (b) 4 only (c) 2 and 4 (d) 2 and 5

Answer is  (c) 2 and 4======it's easier to differentiate when we expand it out.this  expands to      distribute  into      differentiate this function to get the acceleration function (since is just velocity, and rate of change of velocity is acceleration)    find where the acceleration  is equal to zero by setting  to be zero and solving for x.    two integers that multiply to get 8 and add to get -6 are -4 and -2    by the zero product property, either one of these factors can be equal to zero to make the overall product 0 (0 times anything is 0).solutions are t = 4 and t = 2. therefore, choice c.