Step by step
The question
Question: divide (x² + 7x + 10) by (x + 5).
1 Set it up
We write it like long division with numbers.
x + 5 goes outside, x² + 7x + 10 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 + 5) is x² + 5x.
We write it under, with a minus: we take it away.
x² take away x² is 0.
That is why we chose x.
7x take away 5x is 2x.
Bring down the next part: 10.
3 Second part of the answer
Divide the first parts: 2x divided by x is 2.
We write it on top.
Multiply: 2 times (x + 5) is 2x + 10.
We write it under, with a minus: we take it away.
2x take away 2x is 0.
That is why we chose 2.
10 take away 10 is 0.
The last part is 0.
So nothing is left over.
So the answer is x + 2.
Nothing is left over.
4 Check
Let's check with a number: x = 2.
First the start: x² + 7x + 10.
Now the answer: (x + 5) times (x + 2).
Both give 28.
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.