Divide Using Synthetic Division (x^5-15x^4+90x^3-270^2+405x-243)÷(x-3)

$(x^{5} - 15 x^{4} + 90 x^{3} - 270^{2} + 405 x - 243) \div (x - 3)$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0							\xa0

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0							\xa0
	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(3)$ and place the result of $(3)$ under the next term in the dividend $(- 15)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$						\xa0
	$1$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$						\xa0
	$1$	$- 12$

Multiply the newest entry in the result $(- 12)$ by the divisor $(3)$ and place the result of $(- 36)$ under the next term in the dividend $(90)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$					\xa0
	$1$	$- 12$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$					\xa0
	$1$	$- 12$	$54$

Multiply the newest entry in the result $(54)$ by the divisor $(3)$ and place the result of $(162)$ under the next term in the dividend $(0)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$				\xa0
	$1$	$- 12$	$54$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$				\xa0
	$1$	$- 12$	$54$	$162$

Multiply the newest entry in the result $(162)$ by the divisor $(3)$ and place the result of $(486)$ under the next term in the dividend $(0)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$			\xa0
	$1$	$- 12$	$54$	$162$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$			\xa0
	$1$	$- 12$	$54$	$162$	$486$

Multiply the newest entry in the result $(486)$ by the divisor $(3)$ and place the result of $(1458)$ under the next term in the dividend $(- 270^{2})$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$		\xa0
	$1$	$- 12$	$54$	$162$	$486$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$		\xa0
	$1$	$- 12$	$54$	$162$	$486$	$- 71442$

Multiply the newest entry in the result $(- 71442)$ by the divisor $(3)$ and place the result of $(- 214326)$ under the next term in the dividend $(405)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$	$- 214326$	\xa0
	$1$	$- 12$	$54$	$162$	$486$	$- 71442$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$	$- 214326$	\xa0
	$1$	$- 12$	$54$	$162$	$486$	$- 71442$	$- 213921$

Multiply the newest entry in the result $(- 213921)$ by the divisor $(3)$ and place the result of $(- 641763)$ under the next term in the dividend $(- 243)$ .

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$	$- 214326$	$- 641763$
	$1$	$- 12$	$54$	$162$	$486$	$- 71442$	$- 213921$

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

$3$	$1$	$- 15$	$90$	$0$	$0$	$- 270^{2}$	$405$	$- 243$
	\xa0	$3$	$- 36$	$162$	$486$	$1458$	$- 214326$	$- 641763$
	$1$	$- 12$	$54$	$162$	$486$	$- 71442$	$- 213921$	$- 642006$

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

$1 x^{6} + - 12 x^{5} + 54 x^{4} + 162 x^{3} + 486 x^{2} + - 71442 x - 213921 + \frac{- 642006}{x - 3}$

Simplify the quotient polynomial.

$x^{6} - 12 x^{5} + 54 x^{4} + 162 x^{3} + 486 x^{2} - 71442 x - 213921 - \frac{642006}{x - 3}$

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