How do you use synthetic division to divide #( 6x^3 - 9x^2 - 12x - 6 ) / ( 3x + 4 )#?

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Answer 1 · 2016-12-06T10:50:13

The quotient is #=2x^2-17/3x+32/9# and the remainder is #=-182/9#

Let's do the division

#color(white)(aaaa)##6x^3-9x^2-12x-6##color(white)(aaaa)##∣##3x+4#

#color(white)(aaaa)##6x^3+8x^2##color(white)(aaaaaaaaaaaaa)##∣##2x^2-17/3x+32/9#

#color(white)(aaaaa)##0-17x^2-12x#

#color(white)(aaaaaaa)##-17x^2-68/3x#

#color(white)(aaaaaaaaaaa)##0+32/3x-6#

#color(white)(aaaaaaaaaaaaa)##+32/3x+128/9#

#color(white)(aaaaaaaaaaaaaaa)##+0-182/9#

The quotient is #=2x^2-17/3x+32/9# and the remainder is #=-182/9#