Step by step
The question
Question: divide (x² + 4x + 7) by (x + 1).
1 Set it up
We write it like long division with numbers.
x + 1 goes outside, x² + 4x + 7 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 + 1) is x² + x.
We write it under, with a minus: we take it away.
x² take away x² is 0.
That is why we chose x.
4x take away x is 3x.
Bring down the next part: 7.
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 + 1) is 3x + 3.
We write it under, with a minus: we take it away.
3x take away 3x is 0.
That is why we chose 3.
7 take away 3 is 4.
4 has no x.
We can't divide it by x.
So 4 is the remainder: what is left over.
So the answer is x + 3, with 4 left over: plus 4/(x + 1).
4 Check
Let's check with a number: x = 2.
First the start: x² + 4x + 7.
Now the answer: (x + 1) times (x + 3), plus 4.
Both give 19.
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.