[tex]P(x)[/tex] has degree 3, so it takes the general form
[tex]P(x)=ax^3+bx^2+cx+d[/tex]
It has a root [tex]x=1[/tex] of multiplicity 2, which means [tex](x-1)^2[/tex] divides [tex]P(x)[/tex] exactly, and it has a root of [tex]x=-3[/tex] of multiplicity 1 so that [tex]x+3[/tex] also is a factor. So
[tex]P(x)=a(x-1)^2(x+3)[/tex]
Expanding this gives
[tex]P(x)=a(x^3+x^2-5x+3)=ax^3+ax^2-5ax+3a[/tex]
[tex]\implies\begin{cases}a=b\\-5a=c\\3a=d\end{cases}[/tex]
The [tex]y[/tex]-intercept occurs for [tex]x=0[/tex], for which we have
[tex]P(0)=d=2.1[/tex]
Then
[tex]3a=d\implies a=0.7[/tex]
[tex]a=b\implies b=0.7[/tex]
[tex]-5a=c\implies c=-0.14[/tex]
So we have
[tex]\boxed{P(x)=0.7x^3+0.7x^2-0.14x+2.1}[/tex]
