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)

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Solution

$p (x) = x^{3} - 3 x^{2} + x + 2$
$q (x) = x - 24 (r) = - 2 x + 4$ By division algorithm
Dividend = Divisior $\times$ Quotient Remainder $p (x) = q (x) \times g (x) + r (x)$
$x^{3} - 3 x^{2} + x + 2 = (x - 2) \times g (x) + (- 2 x + 4)$ $g (x)$ = $\frac{x^{2} + 3 x^{2} x + 2}{x - 2}$
+ - .............
x - 2
x-2
- +
$∴ D i v i s i o r g (x) = x^{2} - x + 1$

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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).

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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)

p(x)=x3−3x2+x+2q(x)=x−24(r)=−2x+4 By division algorithm Dividend = Divisior × Quotient Remainder p(x)=q(x)×g(x)+r(x)x3−3x2+x+2=(x−2)×g(x)+(−2x+4) g(x) = x2+3x2x+2x−2+ - .............x - 2 x-2 - + ∴Divisiorg(x)=x2−x+1

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)