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:
[tex]\begin{gathered} x=-1 \\ x=\frac{1}{2} \\ x=3 \end{gathered}[/tex]
We can use these roots to get the factors of the polynomial.
Hence, the first factor is
[tex]\begin{gathered} x=-1 \\ \therefore \\ (x+1)\text{ is a factor} \end{gathered}[/tex]
The second factor is
[tex]\begin{gathered} x=\frac{1}{2} \\ 2x=1 \\ \therefore \\ (2x-1)\text{ is a factor} \end{gathered}[/tex]
The third factor is
[tex]\begin{gathered} x=3 \\ \therefore \\ (x-3)\text{ is a factor} \end{gathered}[/tex]
The factors are (x + 1)(2x - 1)(x - 3).
Therefore, OPTION D is correct.
