Bobby 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 (-2𝒙 + 4). Find the divisor.

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Solution

In this question, since we do not know the divisor, we can not apply the long division method.

So let’s apply this: Dividend = Divisor x Quotient + Remainder

=> (  $x^{3}$ - 3 $x^{2}$ + x + 2) = Divisor × (x - 2) + (-2x + 4)
=> Divisor × (x - 2) = ( $x^{3}$ - 3 $x^{2}$ + x + 2) - (-2x + 4)
=> Divisor = ( $x^{3}$ - 3 $x^{2}$ + 3x -2) ÷ (x - 2)

Now apply the long division of these two polynomials as shown below:

We get, Divisor = $x^{2}$ - x + 1.

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Bobby 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.​

Bobby 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 (-2𝒙 + 4). Find the divisor.