How do you long divide #((x^5)-4(x^4)+(x^3)-7x+1 )/( x+2)#?

1 Answer
Tony B
Jul 1, 2016

#x^2-6x^3+13x^2-26x+45-89/(x+2)#

Explanation:

Toa maintain positioning logic (lining up) I introduce place holders such as #0x^2#

#" "x^5-4x^4+x^3+0x^2-7x+1#
#color(magenta)(x^4)(x+2)->" " ul(x^5+2x^4color(white)(.........) larr" "Subtract)#
#" "0-6x^4+x^3+0x^2-7x+1#
#color(magenta)(-6x^3)(x+2)-> ul(-6x^4-12x^3color(white)(.........) larr" "Subtract)#
#" "0+13x^3+0x^2-7x+1#
#color(magenta)(13x^2)(x+2)-> " "ul(13x^3+26x^2" "larr Subtract)#
#" "0-26x^2-7x+1#
#color(magenta)(-26x)(x+2)->" "ul(-26x^2-52x" "larr Subtract)#
#" "0+45x+1#
#color(magenta)(45)(x+2)->" "ul(45x+90" "larr Subtr.#
#" "0color(magenta)(-89)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(magenta)(x^2-6x^3+13x^2-26x+45-89/(x+2))#

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