Question

Use the given factor and the graph of the 3rd degree polynomial to determine the missing factor:One factor is: x^2+2x+2 The graph is:Type the missing factor in the space belowAnswer:

Answer 1

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 :

`f(x)=a(x-b)(x^2+2x+2)`

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 :

`f(x)=a(x+3)(x^2+2x+2)`

Let's find the value of "a" by substituting a point that is on the graph.

Let's say (0, 6)

`\begin{gathered} f(0)=a(0+3)(0^2+2*0+2) \\ 6=a(3)(2) \\ 6=6a \\ a=(6)/(6)=1 \end{gathered}`

Therefore, the missing factor is (x + 3)

ANSWER :

`(x+3)`