# 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=-3, how do you find a possible formula for P(x)?

##### 1 Answer

Apr 21, 2016

#### Explanation:

Each root corresponds to a linear factor, so we can write:

#P(x) = x^2(x-1)^2(x+3)#

#=x^2(x^2-2x+1)(x+3)#

#= x^5+x^4-5x^3+3x^2#

Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this

**Footnote**

Strictly speaking, a value of *root* of *zero* of *zeros* of *roots* of