Symbiosis National Aptitude Test SNAP 2017 Paper

Here, Dividend, p(x) = ${\mathit{x}}^3-3{\mathit{x}}^2$ + x + 2
Divisor = g(x), Quotient = (x - 2) and Remainder = (-2x + 4)
Since, (Quotient × Divisor) + Remainder = Dividend
.-. [(x-2) × g(x)] + [(-2x+4)] = ${\mathit{x}}^3-3{\mathit{x}}^2$ + x + 2
⇒ (x-2) × g(x) = ${\mathit{x}}^3$ - 3 x 2 + x + 2 - (- 2 x + 4)
= ${\mathit{x}}^3$ - 3 x 2 + x + 2 + 2 x - 4
= ${\mathit{x}}^3-3{\mathit{x}}^2$ + 3x - 2
∴ g (x) = $\frac{{\mathit{x}}^3-3{\mathit{x}}^2+3\mathit{x}-2}{\mathit{x}-2}$
Now, dividing ${\mathit{x}}^3-3{\mathit{x}}^2$ + 3x - 2 by x - 2, we have
∴ g (x) = $\frac{{\mathit{x}}^3-3{\mathit{x}}^2+3\mathit{x}-2}{\mathit{x}-2}$ = ${\mathit{x}}^2-\mathit{x}+1$