Use the Remainder Theorem to determine whether x + 1 is a divisor. Show your work.
P(x) = 2x^3 + 4x^2 - 2x + 12
A. x+1 is a divisor of P(x)
B. x+1 is not a divisor of P(x)
C. x+1 is a partial divisor of P(x)
D. Not enough information has been provided
To determine whether x + 1 is a divisor of P(x), we need to determine if P(-1) = 0. If P(-1) = 0, then x + 1 is a divisor.
To find P(-1), substitute -1 into the polynomial:
P(-1) = 2(-1)^3 + 4(-1)^2 - 2(-1) + 12
= 2(-1) + 4(1) + 2 + 12
= -2 + 4 + 2 + 12
= 16
Since P(-1) = 16 and not 0, x + 1 is not a divisor of P(x).
Therefore, the correct answer is B. x + 1 is not a divisor of P(x).