Divide Using Synthetic Division (3x^3-4x^2+5)/(x-3/2)

$\frac{3 x^{3} - 4 x^{2} + 5}{x - \frac{3}{2}}$

Place the numbers representing the divisor and the dividend into a division-like configuration.

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0			\xa0

The first number in the dividend $(3)$ is put into the first position of the result area (below the horizontal line).

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0			\xa0
	$3$

Multiply the newest entry in the result $(3)$ by the divisor $(\frac{3}{2})$ and place the result of $(\frac{9}{2})$ under the next term in the dividend $(- 4)$ .

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$		\xa0
	$3$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$		\xa0
	$3$	$\frac{1}{2}$

Multiply the newest entry in the result $(\frac{1}{2})$ by the divisor $(\frac{3}{2})$ and place the result of $(\frac{3}{4})$ under the next term in the dividend $(0)$ .

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$	$\frac{3}{4}$	\xa0
	$3$	$\frac{1}{2}$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$	$\frac{3}{4}$	\xa0
	$3$	$\frac{1}{2}$	$\frac{3}{4}$

Multiply the newest entry in the result $(\frac{3}{4})$ by the divisor $(\frac{3}{2})$ and place the result of $(\frac{9}{8})$ under the next term in the dividend $(5)$ .

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$	$\frac{3}{4}$	$\frac{9}{8}$
	$3$	$\frac{1}{2}$	$\frac{3}{4}$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{3}{2}$	$3$	$- 4$	$0$	$5$
	\xa0	$\frac{9}{2}$	$\frac{3}{4}$	$\frac{9}{8}$
	$3$	$\frac{1}{2}$	$\frac{3}{4}$	$\frac{49}{8}$

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$3 x^{2} + \frac{1}{2} x + \frac{3}{4} + \frac{\frac{49}{8}}{x - \frac{3}{2}}$

Simplify the quotient polynomial.

$3 x^{2} + \frac{x}{2} + \frac{3}{4} + \frac{49}{4 (2 x - 3)}$

Divide Using Synthetic Division (3x^3-4x^2+5)/(x-3/2)

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