Question

Divide the polynomial 2x^4 -6x^3 +7x^2- 4x-2 by the polynomial 2x^2-2x+1 and
verify the division algorithm.​

Answer 1

$\dfrac{2x^4-6x^3+7x^2-4x-2}{2x^2-2x+1}$

$=x^2+\dfrac{-4x^3+6x^2-4x-2}{2x^2-2x+1}$

$=x^2-2x+\dfrac{2x^2-2x-2}{2x^2-2x+1}$

$=x^2-2x+1+\dfrac{-3}{2x^2-2x+1}$

$=x^2-2x+1-\dfrac{3}{2x^2-2x+1}$