Question

the graph of the fourth - degree polynomial function ( f(x) ) is shown in the coordinate plane below.
based on the graph, which of the following are factors of ( f(x) )? select all that apply.
a. ( (x + 3) )
b. ( (x + 2) )
c. ( (x - 1) )
d. ( (x + 1) )
e. ( (x - 2) )
f. ( (x - 3) )
g. ( (x - 12) )

Explanation:

Step1: Identify x-intercepts

The graph crosses the x-axis at $x=-1$ and $x=2$.

Step2: Convert to linear factors

For intercept $x=a$, factor is $(x-a)$.

• For $x=-1$: $(x-(-1))=(x+1)$
• For $x=2$: $(x-2)$

Step3: Match with options

The factors correspond to options D and E.

Answer:

D. (x+1), E. (x-2)