Question

Which of the following appear to be the linear factors of the polynomial function displayed on the graph

Answer 1

The linear factors can be gotten by picking out the roots from the graph.

The roots are those points where the graph intercepts the x-axis.

From the graph, we have the following values:

`\begin{gathered} x=-1 \\ x=(1)/(2) \\ x=3 \end{gathered}`

We can use these roots to get the factors of the polynomial.

Hence, the first factor is

`\begin{gathered} x=-1 \\ \therefore \\ (x+1)\text{ is a factor} \end{gathered}`

The second factor is

`\begin{gathered} x=(1)/(2) \\ 2x=1 \\ \therefore \\ (2x-1)\text{ is a factor} \end{gathered}`

The third factor is

`\begin{gathered} x=3 \\ \therefore \\ (x-3)\text{ is a factor} \end{gathered}`

The factors are (x + 1)(2x - 1)(x - 3).

Therefore, OPTION D is correct.