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-12color(white)(aaaa)x^2+2x+1

color(white)(aaaa)x^4+2x^3+x^2color(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