Question 465717
For the polynomial below, list each real zero and its multiplicity. Please be sure to show all of your work.
f(x) = 4(x+3)(x-1)³
4(x+3)(x-1)^3=0
4(x+3)(x-1)(x-1)(x-1)=0

x+3=0
x=-3
or
x-1=0
x=1 (multiplicity 3)
see graph as a visual check on the answers
note: when a curve flattens out where one of the zeros are, they are multiple roots.
..


{{{ graph( 300, 300, -4, 4, -100, 10,4(x+3)(x-1)^3) }}}