Question

factorising 6x^3-2x^4+3x^2+3x+2÷3x-x^2+2​

Answer 1

$\small\underbrace\bold\green{Answer:-}$

Factorising :

$\rm\dashrightarrow{ \dfrac{ {6x}^{3} - {2x}^{4} + {3x}^{2} + 3x + 2}{ - {x}^{2} + 3x + 2} }$

$\rm\dashrightarrow{ \dfrac{ { - 2x}^{4} + {6x}^{3} + {3x}^{2} + 3x + 2 }{ - {x}^{2} + 3x + 2} }$

$\rm\dashrightarrow{ \dfrac{ {2x}^{2}( - {x}^{2} + 3x + 1) - 2 + {3x}^{2} + 3x + 2}{ - {x}^{2} +3x + 2 } }$

$\rm\dashrightarrow{ \dfrac{ {2x}^{2} ( - {x}^{2} + 3x + 1) - {x}^{2} + 3x + 2}{ - {x}^{2} + 3x + 2 } }$

$\rm\dashrightarrow{ \dfrac{ {2x}^{2} - {x}^{2} + 3x + 2) + ( - {x}^{2} + 3x + 2) }{ - {x}^{2} + 3x + 2} }$

$\rm\dashrightarrow{ \dfrac{ \cancel{ (- {x}^{2} + 3x + 2}) \: ( {2x}^{2} + 1)}{ \cancel{ - {x}^{2} + 3x + 2}} }$

$\rm\hookrightarrow \red {{2x}^{2} + 1}$

$\rule{92mm}{1mm}$

$\: \bf\green{Learn \: more :-}$

$\begin{gathered}\begin{gathered}\begin{gathered}\small\begin{gathered}\begin{gathered} \bigstar \: \bf \underline{More \: Useful \: formulae} \: \bigstar\\ \begin{gathered} \\ {\boxed{\begin{array}{cccc} \\ {\displaystyle \star\sf{Perimeter \: of \: Triangle }} = \sf{Length +Breadth + Height} \\ \\ \star\sf{Area \: of \: Rectangle = Lenght×Breadth} \\ \\ {\star\small\sf{Perimeter \: of\: Rectangle = 2(Length + Breadth)}} \\ \\ {\star\small \sf{Diagonal \: of \: Rectangle = \sqrt{ {Length }^{2} + { Breadth}^{2} }}} \\ \\ \star\small\sf{Perimeter \: of \: Square = 4a } \\ \\ \star\small\sf{Diagonal \: of \: Square = a \sqrt{2} }\end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

@Shivam