Question

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

Answer 1

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

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

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

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

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

$=2x+\frac{5x+3}{x-2}$

$\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}5x+3\mathrm{\:and\:the\:divisor\:}x-2\mathrm{\::\:}\frac{5x}{x}=5$

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

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

$\mathrm{Remainder}=13$

$=2x+5+\frac{13}{x-2}$