Question

On dividing x3-3x2+x+2,by a polynomial g(x), the quotient and remainder we're x-2 and -2x+4 respectively. Find g(x)

Answer 1

use this relationship and solve that problem
p(x)=g(x)*q(x)+r(x)
now we want g(x) so
g(x)=p(x)-r(x)/q(x)
now substitute the values and u will get the answer

Answer 2

We know that Dividend = Divisor * Quotient + remainder.

Here,

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

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

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

$g(x) = \frac{x^3 - 3x^2 + 3x - 2}{x - 2}$

          x^2  -  x  +  1
        -----------------------------
x - 2)  x^3 - 3x^2 + 3x - 2 ( 

          x^3 - 2x^2

          -------------------------

                    - x^2 + 3x - 2

                    - x^2 + 2x

           --------------------------

                                x - 2

                                x -  2

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

                                  0.


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



Hope this helps!