Which is the graph of the function f(x) = x3 + x2 + x + 1? i’ll give brainlist

We can factor the equation using grouping.



Factor both halves of the equation.



Both groups have a factor of (x+1). We can use the distributive property to find the other factor. That is, ac + bc = (a+b)(c).

So our final factored form is:



Now let's find the roots of the equation. These are the x values where the graph crosses the x axis. To do this, set both factors equal to zero and solve for x.







This factor does not  produce any rational roots because taking the square root of a negative number results in a complex number.





So the equation hass one root of x = -1. This  means that the  graph should cross the x axis at x = -1. Therefore the last picture is the correct graph. Hope this helps!

Option D      

Step-by-step explanation:

Given : Function

To find : Which graph represents the given function.

Solution :

First thing we plot the graph of the function.

We see that graph cuts at point (0,1) and (-1,0) to the coordinates.

From the given graph Option D graph cuts to these points.

Therefore, Option D is correct.

Refer the attached graph A.