Question

The remainder obtained when the polynomial x4-3x3+9x2-27x+81 is divided by x-3 is

Answer 1

$Let \: the \: polynomial :$

$p(x) = x^{4}-3x^{3}+9x^{2}-27x+81$

$If \: (x-3) \:is\: divided \:by \: p(x) \:then \:the$

$remainder \: is \: p(3)$

$p(3) = 3^{4}-3(3^{3})+9(3)^{2}-27\times 3 + 81$

$= 81 - 3 \times 27 + 9\times 9 - 81 + 81$

$= \cancel{81 }-\cancel { 81 }+ \cancel{81 }-\cancel { 81 }+ 81$

$= 81$

Therefore.,

$Required \:remainder = 81$

•••♪