Divide Using Synthetic Division (4x^2+5x-6)÷(x+2)

$(4 x^{2} + 5 x - 6) \div (x + 2)$

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

$- 2$	$4$	$5$	$- 6$

The first number in the dividend $(4)$ is put into the first position of the result area (below the horizontal line).

$- 2$	$4$	$5$	$- 6$

	$4$

Multiply the newest entry in the result $(4)$ by the divisor $(- 2)$ and place the result of $(- 8)$ under the next term in the dividend $(5)$ .

$- 2$	$4$	$5$	$- 6$
		$- 8$
	$4$

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

$- 2$	$4$	$5$	$- 6$
		$- 8$
	$4$	$- 3$

Multiply the newest entry in the result $(- 3)$ by the divisor $(- 2)$ and place the result of $(6)$ under the next term in the dividend $(- 6)$ .

$- 2$	$4$	$5$	$- 6$
		$- 8$	$6$
	$4$	$- 3$

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

$- 2$	$4$	$5$	$- 6$
		$- 8$	$6$
	$4$	$- 3$	$0$

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

$(4) x - 3$

Simplify the quotient polynomial.

$4 x - 3$

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