At which zero will the graph of f(x) = x³ + x^2 – x – 1 bounce off
the x-axis?

Question

At which zero will the graph of f(x) = x³ + x^2 – x – 1 bounce off
the x-axis?

anonymous · Answer

would this be x=1, i graphed it and that's where the line was bouncing off the x-axis

anonymous · Answer

@tcarroll010

anonymous · Answer

You might want to graph that again.  Also, you wouldn't have to graph.  You could factor and realize that the x-axis will be split into 3 areas, meaning that one of the zeros is a zero twice.  And then check the signs of all factors.

anonymous · Answer

Try this one without graphing, or do the graph second as a confirmation after trying to do this one by factoring.  Try to factor that expression.

anonymous · Answer

x=-1 if you mean by "bounce off" that the curve just touches the x axis.
Refer to the attached plot.

anonymous · Answer

If you factor, you will get:

(x - 1)(x + 1)^2

That splits the x-values into :

x < -1       -1 < x < 1          1 < x

Check all factors for each of those areas.  Hint:  you will go from negative to negative when going from one of them to another.  That's the "bounce".

anonymous · Answer

Take a look:

anonymous · Answer

So, on either side of "x = -1" you go from negative to negative.  That's the bounce, not at x = +1.

anonymous · Answer

to be honest idk how to factor

anonymous · Answer

but i will do some practice on it so i can get better

anonymous · Answer

@tcarroll010 thanks for not just giving me the answer, without the steps i wouldn't learn

anonymous · Answer

It is good to learn synthetic division.  It will come in VERY handy in later math and also right now.

anonymous · Answer

You are always welcome.  Also, Robtobey is a great tutor you can always consult.  @robtobey