find the zeros and state multiplicity of each
f(x)=-2(x-5)^4(x+4)^2x^3

Question

find the zeros and state multiplicity of each
f(x)=-2(x-5)^4(x+4)^2x^3

anonymous · Answer

Since (x-5), (x+4), and x are all multiplying each other, we just need to set f(x) to 0 and solve for the zeros...?
For x=5 -> 0=(5-5)(5+4)(5) and etc...

campbell_st · Answer

the polynomial is already factored. 

so when finding the zeros, if any factor is zero, then the polynomial will be zero. 

So to find the zeros, let each factor equal zero and solve for x. 

x - 5 = 0

x + 4 = 0

x^3 = 0

Next the multiplicity

the multiplicity is the power of the factors.... 

in the example 

$$p(x) = x^3(x - 1)^2$$

the zeros or roots occur when 

x = 0         since this was to the 3rd power, the multiplicity is 3

x - 1 = 0    the multiplicity is the same as the power of the factor, multiplicity 2

hope it helps