Use the Remainder Theorem to determine whether x + 1 is a divisor of P(x)=2x3+4x2−2x+12 (1 point) Responses x+1 is a divisor of P(x) x+1 is a divisor of P(x) x+1 is not a divisor of P(x) x+1 is not a divisor of P(x) x+1 is a partial divisor of P(x) x+1 is a partial divisor of P(x) Not enough information has been provided. Not enough information has been provided.
To determine whether x + 1 is a divisor of P(x), we can use the Remainder Theorem. According to the Remainder Theorem, if P(a) = 0, then (x - a) is a factor of P(x).
To apply the Remainder Theorem, we evaluate P(-1):
P(-1) = 2(-1)^3 + 4(-1)^2 - 2(-1) + 12
= -2 + 4 + 2 + 12
= 16
Since P(-1) is not equal to zero, this means that (x + 1) is not a divisor of P(x). Therefore, the correct response is:
x + 1 is not a divisor of P(x)