Step by step
The question
Question: divide (3x³ − 5x + 2) 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: 3, 0, −5, 2.
There is no x² part.
We write 0x², so the columns line up.
2 Bring down the first
The first number comes straight down: 3.
3 Times 1, then add
3 times 1 is 3.
Write it under the next number.
Add: 0 + 3 is 3.
3 times 1 is 3.
Write it under the next number.
Add: −5 + 3 is −2.
−2 times 1 is −2.
Write it under the next number.
Add: 2 + (−2) is 0.
4 Read the answer
The last number is the remainder: 0.
The other numbers are the answer's numbers: 3, 3, −2.
The answer starts one power lower than x³.
So the answer is 3x² + 3x − 2.
Nothing is left over.
5 Check
Let's check with a number: x = 2.
First the start: 3x³ − 5x + 2.
Now the answer: (x − 1) times (3x² + 3x − 2).
Both give 16.
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.