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

Here in the given question,

Dividend $= x^{3} - 3 x^{2} + x + 2$

Quotient $= x - 2$

Remainder $= - 2 x + 4$

Divisor = g(x)

We know that,

Dividend = Quotient $\times$ Divisor + Remainder

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

$\begin{matrix} x - 2 & x^{3} - 3 x^{2} + 3 x - 2 x^{3} - 2 x^{2} - + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - x^{2} + 3 x - 2 - x^{2} + 2 x + - - --------------- - x - 2 x - 2 - + - ---------------- - 0 \end{matrix}$

$∴ g (x) = (x^{2} - x + 1)$

Suggest Corrections

Similar questions

Q. 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).

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

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).