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 $=-182/9$

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