Divide Using Long Polynomial Division (10x^3+46x^2-21x-27)÷(2x^2+8x-9)

$(10 x^{3} + 46 x^{2} - 21 x - 27) \div (2 x^{2} + 8 x - 9)$

Step 1

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

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

Step 2

Divide the highest order term in the dividend $10 x^{3}$ by the highest order term in divisor $2 x^{2}$ .

$5 x$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

Step 3

Multiply the new quotient term by the divisor.

$5 x$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $10 x^{3} + 40 x^{2} - 45 x$

$5 x$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

Step 5

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

$5 x$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

$6 x^{2}$

$24 x$

Step 6

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

$5 x$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

$6 x^{2}$

$24 x$

$27$

Step 7

Divide the highest order term in the dividend $6 x^{2}$ by the highest order term in divisor $2 x^{2}$ .

$5 x$

$3$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

$6 x^{2}$

$24 x$

$27$

Step 8

Multiply the new quotient term by the divisor.

$5 x$

$3$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

$6 x^{2}$

$24 x$

$27$

$6 x^{2}$

$24 x$

$27$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{2} + 24 x - 27$

$5 x$

$3$

$2 x^{2}$

$8 x$

$9$

$10 x^{3}$

$46 x^{2}$

$21 x$

$27$

$10 x^{3}$

$40 x^{2}$

$45 x$

$6 x^{2}$

$24 x$

$27$

$6 x^{2}$

$24 x$

$27$

Step 10

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

						$5 x$	+	$3$
$2 x^{2}$	+	$8 x$	-	$9$		$10 x^{3}$	+	$46 x^{2}$	-	$21 x$	-	$27$
					-	$10 x^{3}$	-	$40 x^{2}$	+	$45 x$
							+	$6 x^{2}$	+	$24 x$	-	$27$
							-	$6 x^{2}$	-	$24 x$	+	$27$
												$0$

Step 11

Since the remander is $0$ , the final answer is the quotient.

$5 x + 3$

Divide Using Long Polynomial Division (10x^3+46x^2-21x-27)÷(2x^2+8x-9)

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