What is the remainder of the following division problem?
Check the final answer first, then review the worked steps.
Problem
What is the remainder of the following division problem?
Answer
1
Step-by-step solution
- Identify the dividend and divisor: The problem shows a long division setup. The dividend is $x+1$ and the divisor is $x$.
- Perform the division: We want to find out how many times $x$ fits into $x+1$. We can see from the setup that $x$ goes into $x$ one time. So, we write $1$ above the division bar.
- Multiply the quotient by the divisor: Multiply the $1$ we just found by the divisor $x$. This gives $1 \cdot x = x$. We write this below the $x$ in the dividend.
- Subtract: Subtract $x$ from the $x$ in the dividend: $x - x = 0$. We write this result below the line.
- Bring down the next term: Bring down the $+1$ from the dividend. We now have $0 + 1$.
- Determine the remainder: The expression $0+1$ is $1$. Since the degree of $1$ (which is 0) is less than the degree of the divisor $x$ (which is 1), we stop here. The remainder is $1$.