Question

On dividing `x^3-3x^2+x+2`by a polynomial the quotient and remainder were `x-2`and `-2x+4`, respectively. Find g(x).

Answer 1

Divident=`(x^3-3x^2+x+2)`
Quotient=(x-2)
Remainder=(-2x+9)
Divisor=g(x)
=Divident=Divisor*quotient+remainder
=`(x^3-3x^2+x+2)=g(x)*(x-2)+(-2x+4)`
after solving this equation
g(x)=`x^2-x+1`