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

Question 1

Question 2

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

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

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

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

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

=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)

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