Priya lost her homework paper on polynomials and she doesn't remember the diviso

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Priya lost her homework paper on polynomials and she doesn't remember the divisor which, on dividing the polynomial $x^{3} - 3 x^{2} + x + 2$ gives quotient $(x - 2)$ and remainder $(- 2 x + 4) .$ Find the divisor.

Options:

A .

5 x^{2} - 7 x + 9

B .

x^{2} - 8 x + 7

C .

x^{2} - x + 1

D .

6 x^{2} - x + 11

Answer: Option C
:
C

We know that,
Dividend = Divisor x Quotient +Remainder
$x^{3} - 3 x^{2} + x + 2 = D i v i s o r \times (x - 2) + (- 2 x + 4)$
$\Rightarrow D i v i s o r \times (x - 2) = x^{3} - 3 x^{2} + x + 2 + 2 x - 4$
$\Rightarrow D i v i s o r = \frac{(x^{3} - 3 x^{2} + 3 x - 2)}{x - 2}$

$∴ D i v i s o r = x^{2} - x + 1$

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