Find the remainder when P(x) = 2x^3 + (-6)x + (2) is divided by x – (-2).
Note
Apply the Remainder Theorem carefully. When a polynomial P(x) is divided by x - a, the remainder is P(a). Here the divisor is x - (-2), so substitute x = -2 into the polynomial. P(-2) = 2(-2)^3 + (-6)(-2) + (2) = -16 + 12 + 2 = -2. Therefore the remainder is -2.