Question

find the zeros and state the multiplicity. f(x)=-4x^2(x-8)(x+4)^3

Answer 1

Set f(x) equal to 0, and then each of its factors...
-4x^2 (x - 8) (x+4)^3 = 0
-4x^2 = 0 x - 8 = 0 x + 4 =0
x^2 = 0 x = 8 x = -4
x = 0

Multiplicity is how many times a number is a zero for the polynomial
ie. There are two 'x', one 'x-8', and three 'x+4" (from the exponents on the factors with x)

So, the full answer would be: x=0 w/ multiplicity 2, x=8, and x=-4 w/ multiplicity 3