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 . 5x2−7x+9

B . x2−8x+7

C . x2−x+1

D . 6x2−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}

Priya Lost Her Homework Paper On Polynomials And She Doesn't...

∴ D i v i s o r = x^{2} - x + 1

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