Find the Quotient (x^2-5x+2)÷(x-3)

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

Step 1

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

$x$

$3$

$x^{2}$

$5 x$

$2$

Step 2

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

					$x$
	$x$	-	$3$		$x^{2}$	-	$5 x$	+	$2$

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 $x^{2} - 3 x$

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 $- 2 x$ 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 $- 2 x + 6$

Step 10

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

Step 11

The quotient is $x - 2$ .

$x - 2$