How do you simplify and divide #(b^3+8b^2-20b)div(b-2)#?
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"What is the equation of a neutralization reaction between sodium hydroxide and hydrochloric acid?"
#b^3+8b^2-20bdivcolor(blue)(b^2+10b)#
#color(white)("XXXXXXXXXXXXX")#with a remainder of #color(red)0#
Using synthetic division:
#{:
(,,color(gray)(b^3),color(gray)(b^2),color(gray)(b^1),color(gray)(b^0)),
(," | ",1,+8,-20,color(white)("x")0),
(+," | ",ul(" "),ul(color(white)("0")2),ul(color(white)("xx")20),ul(color(white)("x")0)),
(xx 2," | ",1,10,color(white)("xx")0,color(white)("x")0),
(,,color(gray)(b^2),color(gray)(b^1),color(white)("x")color(gray)(b^0),color(gray)("R"))
:}#
#(b^3+8b^2-20b)-:(b-2)#
#color(white)(...)color(white)(.......)b^2+10b#
#b-2|overline(b^3+8b^2-20b)#
#color(white)(............)ul(b^3-2b^2)#
#color(white)(......................)10b^2-20b#
#color(white)(......................)ul(10b^2-20b)#
#color(magenta)(b^3+8b^2-20b-:b-2 = b^2+10b#
