How do you use synthetic division to divide $\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1}$ $( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )$ ?

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How do you use synthetic division to divide $\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1}$ $( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )$ ?

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Answer 1 · 2018-07-11T16:50:03

The remainder is $= (\frac{9}{2})$ $=(9/2)$ and the quotient is $= (x^{2} + x - \frac{1}{2})$ $=(x^2+x-1/2)$

Explanation:

Let's perform the synthetic division

Divide by $2$ $2$

$a a a a$ $color(white)(aaaa)$ $- \frac{1}{2}$ $-1/2$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $+ \frac{3}{2}$ $+3/2$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $- \frac{1}{2}$ $-1/2$ $a a a a a$ $color(white)(aaaaa)$ $- \frac{1}{2}$ $-1/2$ $a a a a$ $color(white)(aaaa)$ $\frac{1}{4}$ $1/4$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________________________________________________________##

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $- \frac{1}{2}$ $-1/2$ $a a a a a$ $color(white)(aaaaa)$ $\frac{9}{4}$ $color(red)(9/4)$

The remainder is $= (\frac{9}{2})$ $=(9/2)$ and the quotient is $= (x^{2} + x - \frac{1}{2})$ $=(x^2+x-1/2)$

$\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1} = (x^{2} + x - \frac{1}{2}) + \frac{\frac{9}{4}}{x + \frac{1}{2}}$ $(2x^3+3x^2+4)/(2x+1)=(x^2+x-1/2)+(9/4)/(x+1/2)$

$\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1} = (x^{2} + x - \frac{1}{2}) + \frac{\frac{9}{2}}{2 x + 1}$ $(2x^3+3x^2+4)/(2x+1)=(x^2+x-1/2)+(9/2)/(2x+1)$

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How do you use synthetic division to divide $\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1}$ $( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )$ ?

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Explanation:

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How do you use synthetic division to divide $\frac{2 x^{3} + 3 x^{2} + 4}{2 x + 1}$ $( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )$ ?