Divide Using Long Polynomial Division (2x^2+5x-7)÷(x-1)

$(2 x^{2} + 5 x - 7) \div (x - 1)$

Step 1

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

$x$

$1$

$2 x^{2}$

$5 x$

$7$

Step 2

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

					$2 x$
	$x$	-	$1$		$2 x^{2}$	+	$5 x$	-	$7$

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 $2 x^{2} - 2 x$

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 $7 x$ 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 $7 x - 7$

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.

$2 x + 7$