How do you divide #(x^2+2x-9) / (3x-4) # using polynomial long division?

1 Answer
Tony B
Mar 19, 2016

Have a look at the method used in http://socratic.org/s/asSYFmWU
The values are different but the method is sound.

The solution for this question is: #x/3+10/9-(41)/(9(3x-4))#

Explanation:

Without breaking down the steps:

#" "x/3+10/9-color(blue)(121)/(color(blue)(9)color(green)((3x-4)))#

#" "color(green)(3x-4)" "|bar(" "color(brown)(x^2+2x-9))#
#" "|" "underline(x^2-(4x)/3 -)" Subtract"#
#" "|" "0+(10x)/3 - 9" Bring down the 9"#
#" "|" "underline((10x)/3-40/9 -)" Subtract"#
#" "|" "0-color(blue)(41/9)" Remainder"#

Divide the remainder by #3x-4# giving the last term of:

#-color(blue)(41)/(color(blue)(9)color(green)((3x-4)))#

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