Question

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

Answer 1

`(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)`