Factoring a 4 element polynomial

[mathtwit]

I'm stuck with this:

(x^3 - 4x^2 + x +6) / (x + 1)

I have tried quite a lot of different ways to factor it and I can't find anything that works but the problem suggests it should have a factor of (x+1) somewhere in it.

Thanks in advance!

 

[galactus]

Long divide and you'll end up with a quadratic. You already have 1 of them, (x+1), which says -1 is a factor.

    ----------------------------
x+1|x^3-4x^2+x+6

The quadratic will then factor and you'll have 3 factors, as there should be.

 

[mathtwit]

Thanks very much,

This is for finding a limit in calculus, so I need to end with something that doesn't have x+1 in the denominator or it's undefined. (limit approaches -1)

As I have factored it after division, I have

x^2 - 3x -2 with remainder of 4 / (x + 1)

How can I get rid of the denominator problem now?

 

[Denis]

As I have factored it after division, I have
x^2 - 3x -2 with remainder of 4 / (x + 1)
How can I get rid of the denominator problem now?

That's not correct; you should end up with x^2 - 5x + 6 and no remainder :idea:

 

[galactus]

No, not quite. You must've divided incorrectly.

You should've gotten:

\(\displaystyle x^{2}-5x+6\)

If I understand you correctly, you now have:

\(\displaystyle \L\\\lim_{x\rightarrow{-1}}x^{2}-5x+6\)