How do you simplify #(x^3+3x^2-x+1)-:(x-1)# using long division?

1 Answer
Barney V.
Apr 10, 2017

Quotient#=color(red)(x^2+4x+3# and remainder #=color(red)4#

Explanation:

#color(white)(aaaaaaaaaa)##color(red)(x^2+4x+3##color(white)(aaaaaaaaaaaaa)###

#x-1color(white)(0)")"overline(color(white)(0)x^3+3x^2-x+1#
#color(white)(00000")")underline(color(white)(0)x^3-x^2color(white)(0))#
#color(white)(aaaaaaaaaaa)##4x^2-x#
#color(white)(0000000000")")underline(color(white)(0)4x^2-4xcolor(white)(0))#
#color(white)(aaaaaaaaaaaaaaaaa)##3x+1##color(white)(aaaaaaaaaaaaa)###

#color(white)(0000000000000000")")underline(color(white)(0)3x-3color(white)(0))#
#color(white)(aaaaaaaaaaaaaaaaaaaaaa)##4##color(white)(aaaaaaaaaaaaa)###

Quotient#=color(red)(x^2+4x+3# and remainder #=color(red)4#

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