Question

Without actual division find the remainder obtained when

Answer 1

Let p(x) =

$p(x) = x {}^{3} - 3x {}^{2} - 9x - 5 \\ g(x) = x + 2 \\ by \: the \: remainder \: theorem\: \\ p( - 2) = ( - 2) {}^{3} - 3( - 2){}^{2} - 9( - 2)5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = - 8 - 12 + 18 - 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: = - 25 + 18 = - 7$

-7 is the remainder