Question

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

Answer 1

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)))`