Divide (x^2-2x-37)÷(x^2-3x-40)

$(x^{2} - 2 x - 37) \div (x^{2} - 3 x - 40)$

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

$x^{2}$

$3 x$

$40$

$x^{2}$

$2 x$

$37$

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

							$1$
	$x^{2}$	-	$3 x$	-	$40$		$x^{2}$	-	$2 x$	-	$37$

Multiply the new quotient term by the divisor.

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

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

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

$1 + \frac{x + 3}{x^{2} - 3 x - 40}$