Find the Remainder (x+1)÷x

$(x + 1) \div x$

Step 1

To calculate the remainder, first divide the polynomials.

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

$x$

$0$

$x$

$1$

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

					$1$
	$x$	+	$0$		$x$	+	$1$

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in $x + 0$

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.

$1 + \frac{1}{x}$

Step 2

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

$1$