How do you divide #( x^3+3x^2+4x+12 )/(x^2+2x)#?

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Answer 1 · 2018-06-30T14:48:02

The remainder is #=2x+12# and the quotient is #=x+1#

Perform a long division

#color(white)(aaaa)##x^3+3x^2+4x+12##color(white)(aaaa)##|##x^2+2x#

#color(white)(aaaa)##x^3+2x^2##color(white)(aaaaaaaaaaaaa)##|##x+1#

#color(white)(aaaaa)##0+x^2+4x#

#color(white)(aaaaaaaa)##x^2+2x#

#color(white)(aaaaaaaaa)##0+2x+12#

The remainder is #=2x+12# and the quotient is #=x+1#

#(x^3+3x^2+4x+12)/(x^2+2x)=(x+1)+(2x+12)/(x^2+2x)#