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

We can factor the equation using grouping.

[tex](x^3+x^2) + (x + 1)[/tex]

Factor both halves of the equation.

[tex]x^2(x+1) + 1(x+1)[/tex]

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:

[tex](x^2+1)(x+1)[/tex]

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.

[tex]x^2+1=0[/tex]

[tex]x^2 = -1[/tex]

[tex]x = \sqrt{-1} [/tex]

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

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

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!