Question

The graph is that of a fourth-degree polynomial function. Which of the following correctly shows three factors of the function?

Answer 1

If a polynomial p(x) has zeros x_1, x_2,..., x_n, it can be factorised in the following form:

`p(x)=a\cdot(x-x_1)(x-x_2)\ldots(x-x_n)._{}`

From the graph, we see that the polynomial has the following zeros:

`\begin{gathered} x_1=-3, \\ x_2=2, \\ x_3=5. \end{gathered}`

So we can represent the polynomial as:

`p(x)=a\cdot(x+3)\cdot(x-2)\cdot(x-5).`

The only answer that has the three correct factors is option A.

Answer

A. (x + 3)(x - 2)(x - 5)