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.

Open in App

Solution

We know that,

Dividend = Divisor x Quotient +Remainder

$x^{3} - 3 x^{2} + x + 2 = D i v i s o r \times (x - 2) + (- 2 x + 4)$

$\Rightarrow D i v i s o r \times (x - 2) = x^{3} - 3 x^{2} + x + 2 + 2 x - 4$

$\Rightarrow D i v i s o r = \frac{(x^{3} - 3 x^{2} + 3 x - 2)}{x - 2}$

$∴ D i v i s o r = x^{2} - x + 1$

Suggest Corrections

Similar questions

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.

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. On dividing polynomial

x^{3} - 3 x^{2} + x + 2

by a polynomial

g (x)

, the quotient and remainder were

x - 2

and

- 2 x + 4

, respectively. Find

g (x)

Question 4
On dividing $x^{3} - 3 x^{2} + x + 2$ by a polynomial g(x), the quotient and remainder were $x - 2$ and $- 2 x + 4$ , respectively. Find g(x).

Join BYJU'S Learning Program

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.

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.