Question

Find the remainder when x cube +3xsquare+3x+1is divided by 5+2x

Answer 1

$f(x) = {x}^{3 } +3 {x}^{2} + 3x + 1$

remainder

$= f( \frac{ - 5}{2} )$

$= ( \frac{ - 5}{2 } ) {}^{3} + 3( \frac{ - 5}{2} {)}^{2} + 3( \frac{ - 5}{2} ) + 1$

$\frac{ - 125}{8} + \frac{75}{4} - \frac{15}{2} + 1$

$= \frac{ - 125 + 150 - 60 + 8}{8}$

$\frac{ - 27}{8}$

Answer 2

the remainder will be minus 11 upon 4 and the quotient will be 1 by 2 X square + 3 by 4 x + 3 by 4