Thread: Which of the following is a factor of

1. Which of the following is a factor of

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

2. Use the Factor Theorem, namely that for any Polynomial function $P(x)$, if $P(a) = 0$ then $x - a$ is a factor.

P(x) = (-3)^4+ 6x^(-3)+ 9(-3)^2+ 3(-3) + 9= 0

?

4. Originally Posted by dragovx

P(x) = (-3)^4+ 6x^(-3)+ 9(-3)^2+ 3(-3) + 9= 0

?
You're on the right track.

If you're testing $x + 3$ as a factor, then $P(-3) = 0$...

$P(x) = x^4 + 6x^3 + 9x^2 + 3x + 9$

$P(-3) = (-3)^4 + 6(-3)^3 + 9(-3)^2 + 3(-3) + 9$

$= 81 + 6(-27) + 9(9) - 9 + 9$

$= 81 - 162 + 81 - 9 + 9$

$= 0$ as required.

Therefore $x + 3$ is a factor.

5. Originally Posted by dragovx
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
The rational roots theorem allows the first two to be eliminated with no further consideration and Descartes rule of signs tell you that this has no positive roots which eliminates x-3 leaving only one case to check.

CB