Divide Using Synthetic Division (5x^2+36x+40)÷(x+6)

$(5 x^{2} + 36 x + 40) \div (x + 6)$

Step 1

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

$- 6$	$5$	$36$	$40$
	\xa0		\xa0

Step 2

The first number in the dividend $(5)$ is put into the first position of the result area (below the horizontal line).

Step 3

Multiply the newest entry in the result $(5)$ by the divisor $(- 6)$ and place the result of $(- 30)$ under the next term in the dividend $(36)$ .

Step 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.

Step 5

Multiply the newest entry in the result $(6)$ by the divisor $(- 6)$ and place the result of $(- 36)$ under the next term in the dividend $(40)$ .

Step 6

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

Step 7

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

$(5) x + 6 + \frac{4}{x + 6}$

Step 8

Simplify the quotient polynomial.

$5 x + 6 + \frac{4}{x + 6}$