Divide Using Synthetic Division 2x^4-3x^3-24x^2+76x-60 by 2x-3

$2 x^{4} - 3 x^{3} - 24 x^{2} + 76 x - 60$ by $2 x - 3$

Write the problem as a mathematical expression.

$\frac{2 x^{4} - 3 x^{3} - 24 x^{2} + 76 x - 60}{2 x - 3}$

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{2} \cdot \frac{2 x^{4} - 3 x^{3} - 24 x^{2} + 76 x - 60}{\frac{2 x - 3}{2}}$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0				\xa0

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0				\xa0
	$2$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$			\xa0
	$2$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$			\xa0
	$2$	$0$

Multiply the newest entry in the result $(0)$ by the divisor $(\frac{3}{2})$ and place the result of $(0)$ under the next term in the dividend $(- 24)$ .

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$		\xa0
	$2$	$0$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$		\xa0
	$2$	$0$	$- 24$

Multiply the newest entry in the result $(- 24)$ by the divisor $(\frac{3}{2})$ and place the result of $(- 36)$ under the next term in the dividend $(76)$ .

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$	$- 36$	\xa0
	$2$	$0$	$- 24$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$	$- 36$	\xa0
	$2$	$0$	$- 24$	$40$

Multiply the newest entry in the result $(40)$ by the divisor $(\frac{3}{2})$ and place the result of $(60)$ under the next term in the dividend $(- 60)$ .

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$	$- 36$	$60$
	$2$	$0$	$- 24$	$40$

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

$\frac{3}{2}$	$2$	$- 3$	$- 24$	$76$	$- 60$
	\xa0	$3$	$0$	$- 36$	$60$
	$2$	$0$	$- 24$	$40$	$0$

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

$(\frac{1}{2}) \cdot (2 x^{3} + 0 x^{2} + (- 24) x + 40)$

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (2 x^{3} - 24 x + 40)$

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{2} \cdot (2 x^{3} - 24 x) + \frac{1}{2} \cdot 40$

Apply the distributive property.

$\frac{1}{2} \cdot (2 x^{3}) + \frac{1}{2} \cdot (- 24 x) + \frac{1}{2} \cdot 40$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x^{3}$ .

$\frac{1}{2} \cdot (2 (x^{3})) + \frac{1}{2} \cdot (- 24 x) + \frac{1}{2} \cdot 40$

Cancel the common factor.

$\frac{1}{2} \cdot (2 x^{3}) + \frac{1}{2} \cdot (- 24 x) + \frac{1}{2} \cdot 40$

Rewrite the expression.

$x^{3} + \frac{1}{2} \cdot (- 24 x) + \frac{1}{2} \cdot 40$

Cancel the common factor of $2$ .

Factor $2$ out of $- 24 x$ .

$x^{3} + \frac{1}{2} \cdot (2 (- 12 x)) + \frac{1}{2} \cdot 40$

Cancel the common factor.

$x^{3} + \frac{1}{2} \cdot (2 (- 12 x)) + \frac{1}{2} \cdot 40$

Rewrite the expression.

$x^{3} - 12 x + \frac{1}{2} \cdot 40$

Cancel the common factor of $2$ .

Factor $2$ out of $40$ .

$x^{3} - 12 x + \frac{1}{2} \cdot (2 (20))$

Cancel the common factor.

$x^{3} - 12 x + \frac{1}{2} \cdot (2 \cdot 20)$

Rewrite the expression.

$x^{3} - 12 x + 20$

Divide Using Synthetic Division 2x^4-3x^3-24x^2+76x-60 by 2x-3

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