Question 1147507
<br>
For each root a, you need one or more factors of (x-a).<br>
The simplest is<br>
(1) {{{P(x) = (x-1)(x+1)(x-3)}}}<br>
There can also be a constant factor; for example<br>
(2) {{{P(x) = -2(x-1)(x+1)(x-3)}}}<br>
And any of the linear factors can occur multiple times; for example<br>
(3) {{{P(x) = (x-1)((x+1)^2)((x-3)^3)}}}<br>
Graphs: (1) red; (2) green; (3) blue....<br>
{{{graph(400,400,-2,4,-20,20,(x-1)(x+1)(x-3),-2(x-1)(x+1)(x-3),(x-1)((x+1)^2)((x-3)^3))}}}