y = ( x +8) (x -3) ^4
y = 0
0 = (x +8)
x = -8
The multiplicity of multiple this zero is 1
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y = (x -3) ^4
0 = (x - 3) ^4
0 =(x - 3)
x = 3
In this case, we have a multiplicity
y = (x -3) ^4 = (x-3) (x-3) (x-3) (x-3)
We have four times the same factor, it is repeated
The multiplicity of multiple zeroes is 4
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Answer
zeroes multiplicity
x=3 4
x=-8 1