Synthetic (x^2 + 2x - 8) ÷ (x - 2)

Step by step

The question

Question: divide (x² + 2x − 8) 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, 2, −8.

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: 2 + 2 is 4.

4 times 2 is 8.

Write it under the next number.

Add: −8 + 8 is 0.

4 Read the answer

The last number is the remainder: 0.

The other numbers are the answer's numbers: 1, 4.

The answer starts one power lower than x².

So the answer is x + 4.

Nothing is left over.

5 Check

Let's check with a number: x = 1.

First the start: x² + 2x − 8.

Now the answer: (x − 2) times (x + 4).

Both give −5.

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.