How do you long divide #(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)#?

2 Answers
Dec 10, 2016

The quotient is #=x^2-x-12# and the remainder is #=0#

Explanation:

Let's do the long division

#color(white)(aaaa)##x^4+x^3-13x^2-25x-12##color(white)(aaaa)##∣##x^2+2x+1#

#color(white)(aaaa)##x^4+2x^3+x^2##color(white)(aaaaaaaaaaaaaaa)##∣##x^2-x-12#

#color(white)(aaaa)##0-x^3-14x^2-25x#

#color(white)(aaaaaa)##-x^3-2x^2-x#

#color(white)(aaaaaaaaa)##0-12x^2-24x-12#

#color(white)(aaaaaaaaaaa)##-12x^2-24x-12#

#color(white)(aaaaaaaaaaaaaaa)##-0-0-0#

The quotient is #=x^2-x-12# and the remainder is #=0#

Dec 10, 2016

#x^2-x-12#

Explanation:

#" "x^4+x^3-13x^2-25x-12#
#color(red)(x^2)(x^2+2x+1) -> ul(x^4 +2x^3+x^2" " larr" subtract"#
#" "0 -x^3-14x^2-25x-12#
#color(red)(-x)(x^2+2x+1)->color(white)(.)ul(-x^3-2x^2color(white)(.)-x larr" subtract")#
#" "0-12x^2-24x-12 #
#color(red)(-12)(x^2+2x+1)->" "color(white)(.)ul(-12x^2 -24x-12larr" subtract")#
#" "0" " +0" "+0#

There is no remainder

#(x^4+x^3-13x^2-25x-12)/(x^2+2x+1)" " =" " color(red)(x^2-x-12#