Question

Use the Factor Theorem to determine whether x-2 is a factor of P(x) = -x^4 + x^3 - x + 7.
Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

P(?) =?
is x-2 a factor of P(x)
Is x-2 not a factor pf P(x)

Answer 1

Answer: WE have to find if x + 3 is a factor

Here's how we do it :

x + 3 = 0

x = -3

Plug that in :

(-3)^4 + 2(-3)^3 - 2(-3) - 6

81 - 54 + 6 - 6

27

So, when we divide, we get a remainder of 27. This is not zero.

So, since f(a) was not zero, (x - a) is not a factor

P(-3) = 27 ---> ANSWER

Thus here (x + 3) is NOT a factor ---> ANSWER