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 $g (x)$ .

Open in App

Solution

Dividend = Divisor $\times$ Quotient + Remainder

$x^{3} - 3 x^{2} + x + 2 = g (x) \times (x - 2) + (- 2 x + 4)$

$x^{3} - 3 x^{2} + x + 2 - (- 2 x + 4) = g (x) \times (x - 2)$

$x^{3} - 3 x^{2} + 3 x - 2 = g (x) \times (x - 2)$

$\frac{x^{3} - 3 x^{2} + 3 x - 2}{x - 2} = g (x)$

$x - 2$ $) x^{3} - 3 x^{2} + 3 x - 2 ($ $x^{2} - x + 1$
$x^{3} - 2 x^{2}$
------------------------------------------------------
$- x^{2} + 3 x - 2$
$- x^{2} + 2 x$
------------------------------------------------------
$x - 2$
$x - 2$
-------------------------------------------------------
0

$g (x) = x^{2} - x + 1$

Suggest Corrections

Similar questions

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).

Q. On dividing

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

by polynomial

g (x)

, the quotient and remainder were

x - 2

and

4 - 2 x

respectively, then

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).

On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

Q. Divide the polynomial

p (x)

by the polynomial

g (x)

and find the quotient and remainder.

p (x) = x^{3} - 3 x^{2} + 5 x - 3

g (x) = x^{2} - 2

Join BYJU'S Learning Program

On dividing x3−3x2+x+2 by a polynomial g(x) the quotient and remainder were x−2 and −2x+4 respectively. Find g(x).

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 $g (x)$ .