Divide (x^3 - 8) ÷ (x - 2)

Step by step

The question

Question: divide (x³ − 8) by (x − 2).

1 Set it up

We write it like long division with numbers.

x − 2 goes outside, x³ − 8 inside.

There is no x² and no x part.

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

2 First part of the answer

Divide the first parts: x³ divided by x is x².

We write it on top.

Multiply: x² times (x − 2) is x³ − 2x².

We write it under, with a minus: we take it away.

x³ take away x³ is 0.

That is why we chose x².

0x² take away −2x² is 2x².

Bring down the next part: 0x.

3 Second part of the answer

Divide the first parts: 2x² divided by x is 2x.

We write it on top.

Multiply: 2x times (x − 2) is 2x² − 4x.

We write it under, with a minus: we take it away.

2x² take away 2x² is 0.

That is why we chose 2x.

0x take away −4x is 4x.

Bring down the next part: −8.

4 Third part of the answer

Divide the first parts: 4x divided by x is 4.

We write it on top.

Multiply: 4 times (x − 2) is 4x − 8.

We write it under, with a minus: we take it away.

4x take away 4x is 0.

That is why we chose 4.

−8 take away −8 is 0.

The last part is 0.

So nothing is left over.

So the answer is x² + 2x + 4.

Nothing is left over.

5 Check

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

First the start: x³ − 8.

Now the answer: (x − 2) times (x² + 2x + 4).

Both give −7.

So the answer is right!

Let's look back.

First: set it up.

Then: first part of the answer.

Then: second part of the answer.

Then: third part of the answer.

Last: check.