Question

Find the remainder when x^3+3x^2+3x+1 is divided by x+22/7

Answer 1

$Apply \: remainder \: theorem \\ x + \frac{22}{7} = 0 \\ x = \frac{ - 22}{7} \\Replace \: x \: by \: \frac{ - 22}{7} \: we \: get \\ {x}^{3 } + {3x}^{2} + 3x + 1 \\ ( \frac{ - 22}{7} ) ^{3} + 3( \frac{ - 22}{7} )^{2} + 3( \frac{ - 22}{7} ) + 1 \\ \frac{ - 10648}{343} + \frac{1452}{49} - \frac{ 66}{7} + 1 \\ \frac{ - 10648 + 10164- 3234 + 343}{343} \\ \frac{ - 3375}{343}$

Remainder = -3375/343