Synthetic (x^3 - 27) ÷ (x - 3)

Step by step

The question

Question: divide (x³ − 27) by (x − 3).

1 Write the numbers

x − 3 is 0 when x is 3.

So we use 3.

Then we write just the numbers in front: 1, 0, 0, −27.

There is no x² and no x part.

We write 0x² and 0x, so the columns line up.

2 Bring down the first

The first number comes straight down: 1.

3 Times 3, then add

1 times 3 is 3.

Write it under the next number.

Add: 0 + 3 is 3.

3 times 3 is 9.

Write it under the next number.

Add: 0 + 9 is 9.

9 times 3 is 27.

Write it under the next number.

Add: −27 + 27 is 0.

4 Read the answer

The last number is the remainder: 0.

The other numbers are the answer's numbers: 1, 3, 9.

The answer starts one power lower than x³.

So the answer is x² + 3x + 9.

Nothing is left over.

5 Check

Let's check with a number: x = 2.

First the start: x³ − 27.

Now the answer: (x − 3) times (x² + 3x + 9).

Both give −19.

So the answer is right!

Let's look back.

First: write the numbers.

Then: bring down the first.

Then: times 3, then add.

Then: read the answer.

Last: check.