Divide Using Long Polynomial Division (2X^2-5X-3)÷(X-3)

$(2 X^{2} - 5 X - 3) \div (X - 3)$

Step 1

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

$X$

$3$

$2 X^{2}$

$5 X$

$3$

Step 2

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

					$2 X$
	$X$	-	$3$		$2 X^{2}$	-	$5 X$	-	$3$

Step 3

Multiply the new quotient term by the divisor.

Step 4

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

Step 5

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

Step 6

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

Step 7

Divide the highest order term in the dividend $X$ by the highest order term in divisor $X$ .

Step 8

Multiply the new quotient term by the divisor.

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $X - 3$

Step 10

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

Step 11

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

$2 X + 1$