How do you divide #(x^3-7x^2+17x+13 ) / (2x+1) # using polynomial long division?

1 Answer
Shwetank Mauria
Jan 22, 2017

#(x^3-7x^2+17x+13)/(2x+1) = color(magenta)(1/2x^2-15/4x+83/8+(color(blue)(21/8))/(2x+1) #

Explanation:

#" "x^3-7x^2+17x+13#
#color(magenta)(1/2x^2)(2x+1) ->""ul(x^3+1/2x^2) larr" Subtract"#
#" "0 -15/2x^2+17x+13#
#color(magenta)(-15/4x)(2x+1)->" "color(white)()ul(-15/2x^2-15/4x ) larr" Subtract"#
#" "0+83/4x+13#
#color(magenta)(83/8)(2x+1)->" "color(white)(xxxxxx)ul(83/4x+83/8 ) larr" Subtract"#
#" "color(blue)(0 +21/8) larr" Remainder"#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hence, quotient is #x^3-7x^2+17x+13# and remainder is #21/8# and

#(x^3-7x^2+17x+13)/(2x+1) = color(magenta)(1/2x^2-15/4x+83/8+(color(blue)(21/8))/(2x+1) #

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