Question

How do you divide `(2x^3+7x^2-5x-4) / (2x+1)` using polynomial long division?

Answer 1

Quotient is `x^2+3x-4` and remainder is `0`

Explanation:

`2x^3+7x^2-5x-4`

=`2x^3+x^2+6x^2+3x-8x-4`

=`x^2*(2x+1)+3x*(2x+1)-4*(2x+1)`

=`(2x+1)*(x^2+3x-4)`

Hence quotient is `x^2+3x-4` and remainder is `0`

Answer 2

`x^2+3x-4`

Explanation:

Numerator `->color(white)("d")2x^3+7x^2-5x-4`
`color(magenta)(x^2)(2x+1)-> color(white)("d")ul(2x^3+x^2larr" Subtract"`
`color(white)("dddddddddddddd") 0+6x^2-5x-4`
`color(magenta)(3x)(2x+1)-> color(white)("dddddd") ul(6x^2+3xlarr" Subtract")`
`color(white)("ddddddddddddddddddd")0-8x-4`
`color(magenta)(-4)(2x+1) ->color(white)("ddddddd.d")ul(-8x-4 larr" Subtract")`
`"Remainder"-> color(white)("ddddddddddd")0color(white)("d")+0`

`color(white)("dddddddddddddd")color(magenta)( x^2+3x-4 )`