Step by step
The question
Question: divide (x³ − 4x² + x + 6) by (x + 1).
1 Write the numbers
x + 1 is 0 when x is −1.
So we use −1.
Then we write just the numbers in front: 1, −4, 1, 6.
2 Bring down the first
The first number comes straight down: 1.
3 Times −1, then add
1 times −1 is −1.
Write it under the next number.
Add: −4 + (−1) is −5.
−5 times −1 is 5.
Write it under the next number.
Add: 1 + 5 is 6.
6 times −1 is −6.
Write it under the next number.
Add: 6 + (−6) is 0.
4 Read the answer
The last number is the remainder: 0.
The other numbers are the answer's numbers: 1, −5, 6.
The answer starts one power lower than x³.
So the answer is x² − 5x + 6.
Nothing is left over.
5 Check
Let's check with a number: x = 2.
First the start: x³ − 4x² + x + 6.
Now the answer: (x + 1) times (x² − 5x + 6).
Both give 0.
So the answer is right!
Let's look back.
First: write the numbers.
Then: bring down the first.
Then: times −1, then add.
Then: read the answer.
Last: check.