Divide (x^2 - x - 12) ÷ (x - 4) Step by Step

Step by step

The question

Question: divide (x² − x − 12) by (x − 4).

x² − x − 12x − 4

1 Set it up

We write it like long division with numbers.

x − 4 goes outside, x² − x − 12 inside.

2 First part of the answer

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

We write it on top.

Multiply: x times (x − 4) is x² − 4x.

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

x² take away x² is 0.

That is why we chose x.

−x take away −4x is 3x.

Bring down the next part: −12.

3 Second part of the answer

Divide the first parts: 3x divided by x is 3.

We write it on top.

Multiply: 3 times (x − 4) is 3x − 12.

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

3x take away 3x is 0.

That is why we chose 3.

−12 take away −12 is 0.

The last part is 0.

So nothing is left over.

So the answer is x + 3.

Nothing is left over.

x² − x − 12x − 4 = x + 3

4 Check

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

First the start: x² − x − 12.

Start: 2² − 2 − 12 = 4 − 2 − 12 = −10

Now the answer: (x − 4) times (x + 3).

Answer: (2 − 4) × (2 + 3) = (−2) × (5)

= −10

Both give −10.

So the answer is right!

Both give −10

Let's look back.

First: set it up.

Then: first part of the answer.

Then: second part of the answer.

Last: check.

Answer