Find the remainder when P(x) = 4x^3 + (7)x + (5) is divided by x – (-1).
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 - (-1), so substitute x = -1 into the polynomial. P(-1) = 4(-1)^3 + (7)(-1) + (5) = -4 + -7 + 5 = -6. Therefore the remainder is -6.