Step by step
The question
Question: divide (x³ + 3x² − 4) by (x + 2).
1 Write the numbers
x + 2 is 0 when x is −2.
So we use −2.
Then we write just the numbers in front: 1, 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: 1.
3 Times −2, then add
1 times −2 is −2.
Write it under the next number.
Add: 3 + (−2) is 1.
1 times −2 is −2.
Write it under the next number.
Add: 0 + (−2) is −2.
−2 times −2 is 4.
Write it under the next number.
Add: −4 + 4 is 0.
4 Read the answer
The last number is the remainder: 0.
The other numbers are the answer's numbers: 1, 1, −2.
The answer starts one power lower than x³.
So the answer is x² + x − 2.
Nothing is left over.
5 Check
Let's check with a number: x = 2.
First the start: x³ + 3x² − 4.
Now the answer: (x + 2) times (x² + x − 2).
Both give 16.
So the answer is right!
Let's look back.
First: write the numbers.
Then: bring down the first.
Then: times −2, then add.
Then: read the answer.
Last: check.