Question

How do you divide #(5x^2+12x-9) / (x^2+3x-10) # using polynomial long division?

Answer 1

`5color(white)(.) -color(white)(.) (3x-41)/(x^2+3x-10)`

Explanation:

Given: `(color(blue)(5x^2+12x-9))/(color(green)(x^2_3x-10))`

`color(white)("cmmmmmmmmmmm")color(blue)(5x^2+12x-9)`
`color(red)(5)color(green)((x^2+3x-10)) ->color(white)(.,) ul(5x^2+15x-50) larr "Subtract"`
`color(white)("bbbbbbbbbbbbbbbbbbbb") color(red)(0 -3x+41)larr" Remainder"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`(5x^2+12x-9)/(x^2_3x-10)color(white)(.) = color(white)(.) 5 -(3x-41)/(x^2+3x-10)`