Help With The Factor Theorem

[Figure_skater123]

I was wondering if someone could help me with this question, I have been working on it for a while and I don’t quite understand it but I decided to try it anyways and then I got stuck, so I was thinking someone could help me out. Well here is the question:

The product of four integers is x^4 + 6x^3 + 11x^2 +6x, where x is one of the integers. How are the integers related? Hint: try factoring.

Well this is what I get so far:

x^4 + 6x^3 + 11x^2 +6x
x(x^3 + 6x^2 + 11x +6)

P(x) = x^3 + 6^2 + 11x +6
P(-1) = (-1)^3 + 6(-1)^2 + 11(-1) +6
P(-1) = -1 + 6(1) + 11(-1) +6
P(-1) = -1 + 6 - 11 +6
P(-1) = 0


From the synthetic division I then get P(x) = (x+1)(x^2 + 5x + 6)

And from there I get stuck. I don’t know where to go next, or if i am even doing it right. Could someone help me?

Thank you,
Figure_skater123

 

[Gene]

You are fine so far. If you know the quadratic formula you could use that on (x^2 + 5x + 6)
Or you can continue with synthetic division on it, testing the other factors of 6 or
you can recognize that
(x+a)*(x+b)=x^2+5x+6 and find that a*b=6
a+b=5
and try the factors of 6 to solve these two equations.

 

[Figure_skater123]

Hello. Thank you for your help, I can finally send my assignment in.