Question

Divide the polynomials 2x^2+x+3/x-2

Answer 1

`Divide\:\left(2x^2+x+3\right)/ \left(x-2\right)`

`\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}2x^2+x+3\mathrm{\:and\:the\:divisor\:}x-2\mathrm{\::\:}(2x^2)/(x)=2x`

`\mathrm{Multiply\:}x-2\mathrm{\:by\:}2x:\:2x^2-4x`

`\mathrm{Subtract\:}2x^2-4x\mathrm{\:from\:}2x^2+x+3\mathrm{\:to\:get\:new\:remainder}`

`\mathrm{Remainder}=5x+3`

`=2x+(5x+3)/(x-2)`

`\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}5x+3\mathrm{\:and\:the\:divisor\:}x-2\mathrm{\::\:}(5x)/(x)=5`

`\mathrm{Multiply\:}x-2\mathrm{\:by\:}5:\:5x-10`

`\mathrm{Subtract\:}5x-10\mathrm{\:from\:}5x+3\mathrm{\:to\:get\:new\:remainder}`

`\mathrm{Remainder}=13`

`=2x+5+(13)/(x-2)`