Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of

Question

asked Dec 9, 2023 142k views

1 Answer

Lemek · Answer 1 · 2023-12-15T11:02:01+0000

Let P(x) be the polynomial such that the given set is its solution set.

Now notice that:

$\begin{gathered} x=-(1)/(3)\Rightarrow x+(1)/(3)=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}$

Therefore (x-4) and (3x+1) divide to P(x), then:

$\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}$

Simplifying the above result we get:

Setting k=1 we get that:

Answer: Second option.