If a polynomial p(x) has zeros x_1, x_2,..., x_n, it can be factorised in the following form:
[tex]p(x)=a\cdot(x-x_1)(x-x_2)\ldots(x-x_n)._{}[/tex]
From the graph, we see that the polynomial has the following zeros:
[tex]\begin{gathered} x_1=-3, \\ x_2=2, \\ x_3=5. \end{gathered}[/tex]
So we can represent the polynomial as:
[tex]p(x)=a\cdot(x+3)\cdot(x-2)\cdot(x-5).[/tex]
The only answer that has the three correct factors is option A.
Answer
A. (x + 3)(x - 2)(x - 5)
