Question

How do you find the quotient of `(6x^3+5x^2+9)div(2x+3)` using long division?

Answer 1

Quotient: `3x^2-2x+3`
(see below for derivation using long division)

Explanation:

`color(white)("XXXxX")underline(color(white)("x")3x^2color(white)("x")-2xcolor(white)("xx")+3color(white)("XXXX"))`
`2x+3color(white)("x"))color(white)("x")6x^3color(white)("x")+5x^2color(white)("x")+0xcolor(white)("x")+9`
`color(white)("XXXXXX")ul(6x^3color(white)("x")+9x^2)`
`color(white)("XXXXXXXXX")-4x^2color(white)("x")+0x`
`color(white)("XXXXXXXXX")ul(-4x^2color(white)("x")-6x)`
`color(white)("XXXXXXXXXXXXXXX")6xcolor(white)("x")+9`
`color(white)("XXXXXXXXXXXXXXX")ul(6xcolor(white)("x")+9)`
`color(white)("XXXXXXXXXXXXXXXXXXX")0`