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.

$5 x^{2} - 7 x + 9$

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$x^{2} - 8 x + 7$

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$x^{2} - x + 1$

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$6 x^{2} - x + 11$

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Solution

The correct option is C
$x^{2} - x + 1$

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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Similar questions

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

Q. 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

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Find the divisor.

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by a polynomial g (x), the quotient and remainder were

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Priya lost her homework paper on polynomials and she doesn't remember the divisor which, on dividing the polynomial x3−3x2+x+2 gives quotient (x−2) and remainder (−2x+4). Find the divisor.

The correct option is C x2−x+1 We know that, Dividend = Divisor x Quotient +Remainder x3−3x2+x+2=Divisor×(x−2)+(−2x+4) ⇒Divisor×(x−2)=x3−3x2+x+2+2x−4 ⇒Divisor=(x3−3x2+3x−2)x−2 ∴Divisor=x2−x+1

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.