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

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

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Answer 1 · 2016-12-06T10:50:13

The quotient is $= 2 x^{2} - \frac{17}{3} x + \frac{32}{9}$ $=2x^2-17/3x+32/9$ and the remainder is $= - \frac{182}{9}$ $=-182/9$

Explanation:

Let's do the division

$a a a a$ $color(white)(aaaa)$ $6 x^{3} - 9 x^{2} - 12 x - 6$ $6x^3-9x^2-12x-6$ $a a a a$ $color(white)(aaaa)$ $∣$ $∣$ $3 x + 4$ $3x+4$

$a a a a$ $color(white)(aaaa)$ $6 x^{3} + 8 x^{2}$ $6x^3+8x^2$ $a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $∣$ $∣$ $2 x^{2} - \frac{17}{3} x + \frac{32}{9}$ $2x^2-17/3x+32/9$

$a a a a a$ $color(white)(aaaaa)$ $0 - 17 x^{2} - 12 x$ $0-17x^2-12x$

$a a a a a a a$ $color(white)(aaaaaaa)$ $- 17 x^{2} - \frac{68}{3} x$ $-17x^2-68/3x$

$a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ $0 + \frac{32}{3} x - 6$ $0+32/3x-6$

$a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $+ \frac{32}{3} x + \frac{128}{9}$ $+32/3x+128/9$

$a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaa)$ $+ 0 - \frac{182}{9}$ $+0-182/9$

The quotient is $= 2 x^{2} - \frac{17}{3} x + \frac{32}{9}$ $=2x^2-17/3x+32/9$ and the remainder is $= - \frac{182}{9}$ $=-182/9$

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

1 Answer

Explanation:

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How do you use synthetic division to divide ( 6x^3 - 9x^2 - 12x - 6 ) / ( 3x + 4 )6x3−9x2−12x−63x+4( 6x^3 - 9x^2 - 12x - 6 ) / ( 3x + 4 )?

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