Step by step
The question
Question: divide (2x³ − 3x² + 4) 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: 2, −3, 0, 4.
There is no x part.
We write 0x, so the columns line up.
2 Bring down the first
The first number comes straight down: 2.
3 Times −1, then add
2 times −1 is −2.
Write it under the next number.
Add: −3 + (−2) is −5.
−5 times −1 is 5.
Write it under the next number.
Add: 0 + 5 is 5.
5 times −1 is −5.
Write it under the next number.
Add: 4 + (−5) is −1.
4 Read the answer
The last number is the remainder: −1.
The other numbers are the answer's numbers: 2, −5, 5.
The answer starts one power lower than x³.
So the answer is 2x² − 5x + 5, with −1 left over: minus 1/(x + 1).
5 Check
Let's check with a number: x = 2.
First the start: 2x³ − 3x² + 4.
Now the answer: (x + 1) times (2x² − 5x + 5), minus 1.
Both give 8.
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.