Answer:
y = x³ +x² -20x
Step-by-step explanation:
You want a polynomial with roots x ∈ {0, -5, 4}.
Factors
When a polynomial has a root p, it has a factor (x -p). The three given roots mean the polynomial you want can be factored as ...
y = (x -0)(x -(-5))(x -4) = x(x+5)(x-4)
When this product is expanded, the result is ...
y = x³ +x² -20x . . . . polynomial with roots {0, -5, 4}
