Step by step
The question
Question: divide (x³ + 27) by (x + 3).
1 Set it up
We write it like long division with numbers.
x + 3 goes outside, x³ + 27 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 + 3) is x³ + 3x².
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 3x² is −3x².
Bring down the next part: 0x.
3 Second part of the answer
Divide the first parts: −3x² divided by x is −3x.
We write it on top.
Multiply: −3x times (x + 3) is −3x² − 9x.
We write it under, with a minus: we take it away.
−3x² take away −3x² is 0.
That is why we chose −3x.
0x take away −9x is 9x.
Bring down the next part: 27.
4 Third part of the answer
Divide the first parts: 9x divided by x is 9.
We write it on top.
Multiply: 9 times (x + 3) is 9x + 27.
We write it under, with a minus: we take it away.
9x take away 9x is 0.
That is why we chose 9.
27 take away 27 is 0.
The last part is 0.
So nothing is left over.
So the answer is x² − 3x + 9.
Nothing is left over.
5 Check
Let's check with a number: x = 2.
First the start: x³ + 27.
Now the answer: (x + 3) times (x² − 3x + 9).
Both give 35.
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.