Question 1052680
The multiplicity is determined by the exponent of the factor that produced the root. So the factor for the multiplicity 1 root will be a first order polynomial and the multiplicity 3 root will have a third order polynomial.  We are given the two roots and we must have the leading coefficient equal to 1, so we can factor the polynomial in the following way: (x-1)^3(x-2) = 0.  This can be further written as (x-1)(x-1)(x-1)(x-2), which makes it easy to see the multiplicity.  Setting this equal to zero we see that this gives the correct roots, 1 (mult. 3) and 2 (mult. 1). 
Carrying out the multiplication gives f(x)= x^4-5x^3+9x^2-7x+2

The graph is shown below:

{{{ graph( 500, 400, -1, 3, -0.5, 2, (x-1)^3*(x-2)) }}}