What is the quotient when #2x^3 + x + 3# is divided by x + 1?

1 Answer
Alan P.
Jan 5, 2016

#(2x^3+x+3)div(x+1) = color(blue)(2x^2-2x+3)#
#color(white)("XXXXXXXX")# with a #color(green)("R")#emainder #= color(green)(0)#

Explanation:

Using synthetic division:
#(2x^3+x+3) div (xcolor(red)(+)1)#

#{: (,,color(brown)(x^3),color(white)("X")color(brown)(x^2),color(white)("X")color(brown)(x^1),color(white)("X")color(brown)(x^0)), (,"|",2,color(white)("X")0,color(white)("X")1,color(white)("X")3), (,"|",,-2,+2,-3), (bar(color(white)("XXX")),,bar(color(white)("XXX")),bar(color(white)("XXX")),bar(color(white)("XXX")),bar(color(white)("XXX"))), (xx (color(red)(-)1),"|",color(blue)(2),color(blue)(-2),color(white)("X")color(blue)(3),color(white)("X")color(green)(0)), (,,color(brown)(x^2),color(white)("X")color(brown)(x^1),color(white)("X")color(brown)(x^0), color(white)("X")color(green)(R)) :}#

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