From the problem, we have the graph of a 3rd degree polynomial.
One factor is given which is in the 2nd degree.
So the missing factor must be in the 1st degree since the maximum factors of a 3rd degree polynomial is 3.
The function can be written as :
[tex]f(x)=a(x-b)(x^2+2x+2)[/tex]
where a(x - b) is the missing factor.
Factors are also zeros in which the graph intersects the x-axis.
From the graph, it it intersects at point (-3, 0)
So the other factor is (x + 3)
That will be :
[tex]f(x)=a(x+3)(x^2+2x+2)[/tex]
Let's find the value of "a" by substituting a point that is on the graph.
Let's say (0, 6)
[tex]\begin{gathered} f(0)=a(0+3)(0^2+2\times0+2) \\ 6=a(3)(2) \\ 6=6a \\ a=\frac{6}{6}=1 \end{gathered}[/tex]
Therefore, the missing factor is (x + 3)
ANSWER :
[tex](x+3)[/tex]
