Divide (12a^3-3a^2-5a+14)/(4a+3)

$\frac{12 a^{3} - 3 a^{2} - 5 a + 14}{4 a + 3}$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$4 a$

$3$

$12 a^{3}$

$3 a^{2}$

$5 a$

$14$

Step 2

Divide the highest order term in the dividend $12 a^{3}$ by the highest order term in divisor $4 a$ .

					$3 a^{2}$
	$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$

Step 3

Multiply the new quotient term by the divisor.

				$3 a^{2}$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			+	$12 a^{3}$	+	$9 a^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $12 a^{3} + 9 a^{2}$

				$3 a^{2}$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$3 a^{2}$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$

Step 6

Pull the next terms from the original dividend down into the current dividend.

				$3 a^{2}$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$

Step 7

Divide the highest order term in the dividend $- 12 a^{2}$ by the highest order term in divisor $4 a$ .

				$3 a^{2}$	-	$3 a$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$

Step 8

Multiply the new quotient term by the divisor.

				$3 a^{2}$	-	$3 a$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					-	$12 a^{2}$	-	$9 a$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 12 a^{2} - 9 a$

				$3 a^{2}$	-	$3 a$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$

Step 10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$3 a^{2}$	-	$3 a$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$

Step 11

Pull the next terms from the original dividend down into the current dividend.

				$3 a^{2}$	-	$3 a$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$	+	$14$

Step 12

Divide the highest order term in the dividend $4 a$ by the highest order term in divisor $4 a$ .

				$3 a^{2}$	-	$3 a$	+	$1$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$	+	$14$

Step 13

Multiply the new quotient term by the divisor.

				$3 a^{2}$	-	$3 a$	+	$1$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$	+	$14$
							+	$4 a$	+	$3$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $4 a + 3$

				$3 a^{2}$	-	$3 a$	+	$1$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$	+	$14$
							-	$4 a$	-	$3$

Step 15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$3 a^{2}$	-	$3 a$	+	$1$
$4 a$	+	$3$		$12 a^{3}$	-	$3 a^{2}$	-	$5 a$	+	$14$
			-	$12 a^{3}$	-	$9 a^{2}$
					-	$12 a^{2}$	-	$5 a$
					+	$12 a^{2}$	+	$9 a$
							+	$4 a$	+	$14$
							-	$4 a$	-	$3$
									+	$11$

Step 16

The final answer is the quotient plus the remainder over the divisor.

$3 a^{2} - 3 a + 1 + \frac{11}{4 a + 3}$

Divide (12a^3-3a^2-5a+14)/(4a+3)

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