Since the polynomial has to be the simplest, it must be of the form:
[tex]P(x)=(x+2)(x-4)(x-5)\text{.}[/tex]
Multiplying the binomials we get:
[tex]\begin{gathered} P(x)=(x^2-2x-8)(x-5) \\ =x^3-5x^2-2x^2+10x-8x+40. \end{gathered}[/tex]
Simplifying the above polynomial we get:
[tex]P(x)=x^3-7x^2+2x+40.[/tex]
Answer:
[tex]P(x)=x^3-7x^2+2x+40.[/tex]
