Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$ in the following:

$f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12,\ g(x)\ =\ x^2\ –\ 2x\ +\ 2$

Given:

 

$f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12$ and $g(x)\ =\ x^2\ –\ 2x\ +\ 2$.

To do:

We have to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$.

 

Solution:

 

Dividend$f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12$

 

Divisor$g(x)\ =\ x^2\ –\ 2x\ +\ 2$

$x^2 – 2x + 2$)$15x^3 – 20x^2 + 13x – 12$($15x+10$

                            $15x^3 - 30x^2  + 30x$

                         ------------------------------------

                                         $10x^2 - 17x - 12$

                                         $10x^2 - 20x + 20$

                                        --------------------------

                                                        $3x - 32$ 

Therefore,

 $q(x)=15x+10$.

$r(x)=3x - 32$.