Use the Remainder Theorem to determine whether x + 1 is a divisor of P(x)=2x^3+4x^2−2x+12
To determine whether x + 1 is a divisor of P(x) = 2x^3 + 4x^2 − 2x + 12 using the Remainder Theorem, we need to find the remainder when P(-1) is divided by x + 1.
To find P(-1), substitute -1 for x in the polynomial:
P(-1) = 2(-1)^3 + 4(-1)^2 − 2(-1) + 12
= 2(-1) + 4(1) + 2 + 12
= -2 + 4 + 2 + 12
= 16
Therefore, when P(-1) is divided by x + 1, the remainder is 16.
Since the remainder is not zero, x + 1 is not a divisor of P(x).