Question

Find the zeros of the polynomial function and state the multiplicity of each.

4(x + 4)3(x - 4)(x - 2 + i)

Answer 1

So, to find the zeroes, we set the expression equal to zero and solve for the x's:
4(x + 4)^3 (x - 4) (x - 2 + i) = 0
(x + 4)^3 (x - 4) (x - 2 + i) = 0
To get 0, the individual factors must equal 0. So, we solve for x in these cases:
x + 4 = 0
x - 4 = 0
x - 2 + i = 0

The multiplicity is just how many times the factor occurs in the polynomial. E.g., the first is cubed so it occurs three times, therefore the multiplicity is 3 of that root.