Does anyone know how to do this I’m confused

The simplest polynomial with these roots is

f(x) = (x + 1)² (x - 3)

Expand the right side:

f(x) = x³ - x² - 5x - 3

So one sequence of coefficients (the answers you have to fill in) might be {+1, -1, -5, -3}.

If those choices aren't available, you can also multiply f(x) by any appropriate constant c, since both

(x + 1)² (x - 3)

and

c (x + 1)² (x - 3)

and by extension, so would

c f(x) = c x³ - c x² - 5c x - 3c

have the same roots.

For example, if you pick c = -1, then you could submit {-1, +1, +5, +3}. If c = 2, then you could use {+2, -2, -10, -6}. And so on.

idk lol

step-by-step explanation: