Question

find the quotient and remainder when P of x is equal to 3 x cube + x square + 2 X + 5 is divided by g f x is equal to X square + 2 X + 1​

Answer 1

GIVEN :

The expression is $P(x)= 3 x^3 + x ^2 + 2 x + 5$ is divided by $g(x)=x^2 + 2x + 1$

TO FIND :

The quotient and remainder ​ when  $P(x)= 3 x^3 + x ^2 + 2 x + 5$ is divided by $g(x)=x^2 + 2x + 1$

SOLUTION :

Given that  $P(x)= 3 x^3 + x ^2 + 2 x + 5$ is divided by $g(x)=x^2 + 2x + 1$

By using Long Division method we can solve this

                           3x-5

                  ________________________

$x^2+2x+1 ) 3x^3+x ^2+2x+5$

                  $3x^3+6x^2+3x$

           ___(-)___(-)___(-)___________

                           $-5x^2-x+5$

                           $-5x^2-10x-5$

                     ___(+)___(+)__(+)________

                                        9x+10

                      ______________________

∴ the quotient is 3x-5 and the remainder is 9x+10  $P(x)= 3 x^3 + x ^2 + 2 x + 5$ is divided by $g(x)=x^2 + 2x + 1$

∴ the quotient is 3x-5 and the remainder is 9x+10.