Question

On dividing x3 – 3x2 + x + 2 by polynomials g(x), the quotient & remainder were x – 2 & – 2x+4 respectively. Find g(x).

Answer 1

Answer:

$g(x)=x^2-x+1$

Step-by-step explanation:

$x^3-3x^2+x+2=(x-2)g(x)-2x+4$

$x^3-3x^2+3x-2=(x-2)g(x)$

2|      $1$      $-3$      $3$      $-2$

 |                 $2$     $-2$       $0$

  ---------------------------------

           $1$      $-1$      1        0

                                  ------

∴$g(x)=x^2-x+1$