# The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-1 Find a possible formula for P(x)?

##### 1 Answer

Feb 8, 2018

# P(x) = x^2(x-1)^2(x+1) #

#### Explanation:

Given that we have a root of multiplicity

Given that we have a root of multiplicity

Given that we have a root of multiplicity

We are given that

# P(x) = 0 => x^2(x-1)^2(x+1) = 0 #

And we can therefore write

# P(x) = Ax^2(x-1)^2(x+1) #

We also know that the leading coefficient is

Hence,

# P(x) = x^2(x-1)^2(x+1) #