# How do you find all the zeros of #P(x) = (x-5)^2(x+2)^3(x+4)#?

##### 1 Answer

May 28, 2016

#### Answer:

Note that

#5# (multiplicity#2# )

#-2# (multiplicity#3# )

#-4#

#### Explanation:

#=(x-5)(x-5)(x+2)(x+2)(x+2)(x+4)#

Note that

So the only zeros are:

#x=5# with multiplicity#2# #x=-2# with multiplicity#3# #x=-4# with multiplicity#1#

Essentially, finding the zeros of a polynomial (with their multiplicities) is the same as finding the linear factors of that polynomial. If