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

1 Answer
Mar 15, 2017

Answer:

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#