Which of the following is a factor of?
P(x) = x^4+ 6x^3+ 9x^2+ 3x + 9 ?
a) x - 2
b) x + 2
c) x + 3
d) x - 3
e) None of the above
You're on the right track.
If you're testing $\displaystyle x + 3$ as a factor, then $\displaystyle P(-3) = 0$...
$\displaystyle P(x) = x^4 + 6x^3 + 9x^2 + 3x + 9$
$\displaystyle P(-3) = (-3)^4 + 6(-3)^3 + 9(-3)^2 + 3(-3) + 9$
$\displaystyle = 81 + 6(-27) + 9(9) - 9 + 9$
$\displaystyle = 81 - 162 + 81 - 9 + 9$
$\displaystyle = 0$ as required.
Therefore $\displaystyle x + 3$ is a factor.