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.
The Remainder Theorem states that if a polynomial P(x) is divided by a linear divisor of the form (x - c), then the remainder of this division is equal to P(c).
To determine if x + 1 is a divisor of the polynomial P(x) = 2x^3 + 4x^2 - 2x + 12, we need to evaluate P(x) at x = -1, since x + 1 can be rewritten as (x - (-1)).
Let's calculate P(-1):
P(-1) = 2(-1)^3 + 4(-1)^2 - 2(-1) + 12
= 2(-1) + 4(1) + 2 + 12
= -2 + 4 + 2 + 12
= 2 + 12
= 14
Since P(-1) is not equal to 0, we can conclude that x + 1 is not a divisor of P(x). Therefore, the correct response is:
x + 1 is not a divisor of P(x)