Step by step
The question
Question: divide (x² + 5x + 6) by (x + 2).
1 Set it up
We write it like long division with numbers.
x + 2 goes outside, x² + 5x + 6 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 + 2) is x² + 2x.
We write it under, with a minus: we take it away.
x² take away x² is 0.
That is why we chose x.
5x take away 2x is 3x.
Bring down the next part: 6.
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 + 2) is 3x + 6.
We write it under, with a minus: we take it away.
3x take away 3x is 0.
That is why we chose 3.
6 take away 6 is 0.
The last part is 0.
So nothing is left over.
So the answer is x + 3.
Nothing is left over.
4 Check
Let's check with a number: x = 2.
First the start: x² + 5x + 6.
Now the answer: (x + 2) times (x + 3).
Both give 20.
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.
Last: check.