The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is

The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is

Answer Details

Let f(p) = 6p3 - p2 - 47p + 30
Then by the remainder theorem,
(p - 3): f(3) = remainder R,
i.e. f(3) = 6(3)3 - (3)2 - 47(3) + 30 = R
162 - 9 - 141 + 30 = R
192 - 150 = R
R = 42