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

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Solution

We know that the division algorithm states that:
Dividend $= ($ Divisor $\times$ quotient $) +$ Remainder

Here it is given that the dividend is $p (x) = x^{3} - 3 x^{2} + x + 2$ , the divisor is $g (x)$ , the quotient is $x - 2$ and the remainder is $- 2 x + 4$ , therefore,

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

The division is shown above.

Hence, from the above division, we get that the divisor is $g (x) = x^{2} - x + 1$

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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. 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

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder of the following.

$p (x) = x^{3} - 3 x^{2} + 5 x - 3$ and $g (x) = x^{2} - 2$ .

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

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