Question

I need help with this question please.Fyi this is a part of a homework practice

Answer 1

Since the polynomial has to be the simplest, it must be of the form:

`P(x)=(x+2)(x-4)(x-5)\text{.}`

Multiplying the binomials we get:

`\begin{gathered} P(x)=(x^2-2x-8)(x-5) \\ =x^3-5x^2-2x^2+10x-8x+40. \end{gathered}`

Simplifying the above polynomial we get:

`P(x)=x^3-7x^2+2x+40.`

Answer:

`P(x)=x^3-7x^2+2x+40.`