Question

(2x^4 - 3x^3 - 3x^2 +6x -2) : (x^2 -2)

Answer 1

\(\dfrac{\left(2x^4-3x^3-3x^2+6x-2\right)}{x^2-2}\)

= \(\dfrac{\left(2x^4-2x^3-x^3+x^2-4x^2+4x+2x-2\right)}{x^2-2}\)

= \(\dfrac{2x^3\left(x-1\right)-x^2\left(x-1\right)-4x\left(x-1\right)+2\left(x-1\right)}{x^2-2}\)

= \(\dfrac{\left(2x^3-x^2-4x+2\right)\left(x-1\right)}{x^2-2}\)

= \(\dfrac{\left[x^2\left(2x-1\right)-2\left(2x-1\right)\left(x-1\right)\right]}{x^2-2}\)

= \(\dfrac{\left(x^2-2\right)\left(2x-1\right)\left(x-1\right)}{x^2-2}\)

= \(\left(2x-1\right)\left(x-1\right)\)

= \(2x^2-3x+1\)