Question

What must be a factor if the polynomial function f(x) graphed ib the coordinate plane below ?

Answer 1

The question gives us a graph that crosses the x-axis at 3 points: x = 1, x = 2, and x = -3. We are asked to find which of the factors on the graph is in the options given.

- Whenever a graph crosses the x-axis at a point "a", it implies that x = a is a root of the graph and as a result, (x - a) must be a factor of the graph.

- We can apply this to the question and derive the factors of the graph as follows:

`\begin{gathered} \text{ When }x=-3\colon \\ x=-3 \\ \text{Add 3 to both sides} \\ x+3=0 \\ \\ \text{Thus, }(x+3)\text{ is a factor of the graph.} \\ \\ \\ \text{When }x=1\colon \\ x=1 \\ \text{Subtract 1 from both sides} \\ x-1=0 \\ \\ \text{Thus, }(x-1)\text{ is a factor of the graph} \\ \\ \\ \text{When }x=2\colon \\ x=2 \\ \text{Subtract 2 from both sides} \\ x-2=0 \\ \\ \text{Thus, (}x-2)\text{ is a factor of the graph.} \\ \\ \\ \text{Thus, we can conclude that the 3 factors of the graph are:} \\ (x+3),(x+1),\text{ and }(x-2) \end{gathered}`

- Going through the options, we can see that only (x - 1) is present in the options.

- Thus, (x - 1) is the answer

Final Answer

(x - 1) is the answer (OPTION B)